problem solving math for grade 7

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Grade 7 maths problems with answers.

Grade 7 math word problems with answers are presented. Some of these problems are challenging and need more time to solve. The Solutions and explanatiosn are included.

• In a bag full of small balls, 1/4 of these balls are green, 1/8 are blue, 1/12 are yellow and the remaining 26 white. How many balls are blue?
• In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old?
• If the length of the side of a square is doubled, what is the ratio of the areas of the original square to the area of the new square?
• The division of a whole number N by 13 gives a quotient of 15 and a remainder of 2. Find N.

• A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters.
• A car is traveling 75 kilometers per hour. How many meters does the car travel in one minute?
• Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $200, what were her original savings?
• Stuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $30, what was the final price of the sweater?
• 15 cm is the height of water in a cylindrical container of radius r. What is the height of this quantity of water if it is poured into a cylindrical container of radius 2r?
• John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $16, what was the price before the first discount?
• How many inches are in 2000 millimeters? (round your answer to the nearest hundredth of of an inch).
• The rectangular playground in Tim's school is three times as long as it is wide. The area of the playground is 75 square meters. What is the primeter of the playground?
• John had a stock of 1200 books in his bookshop. He sold 75 on Monday, 50 on Tuesday, 64 on Wednesday, 78 on Thursday and 135 on Friday. What percentage of the books were not sold?
• N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to N? A) 1 1/2 B) 1 1/3 C) 5/3 D) 3/2
• In 2008, the world population is about 6,760,000,000. Write the 2008 world population in scientific notation.
• Calculate the circumference of a circular field whose radius is 5 centimeters.

Answers to the Above Problems

• 6 balls are blue
• 10 students are 10 years old
• x = 5/6 meter
• 20,000 square meters
• 368 square units
• 1250 meters per minute
• 78.74 inches
• 40 square meters
• 10π centimeters

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• Students learn about ratios, mixed properties, statistics and other seventh grade skills.
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7th Grade Math Word Problems

Related Pages More Math Word Problems Algebra Word Problems More Singapore Math Word Problems 7th Grade Math Word Problems 2

In these lessons, we will look at some examples of 7th grade word problems with answers, solved using the Singapore Math block diagram method as well as using Algebra.

The following are some examples of 7th Grade Math Word Problems that deals with ratio and proportions.

These are Grade 7 word problems from a Singapore text. The problems are solved both using algebra (the way it is generally done in the US) and using block diagrams (the way it was shown in the Singapore text). You can then decide which one you prefer.

Singapore Math 2 (A Grade 7 Algebra Word Problem from a Singapore text)

Example: Mr. Rozario bought some apples and oranges. The ratio of the number of apples to the number of oranges are 2:5. He gave 3/4 of the apples to his sister and 34 oranges to his brother. The ratio of the number of apples to the number of oranges that he has now is 2:3. How many apples did Mr. Rozario buy? How many oranges did Mr. Rozario buy?

Example: At first, the ratio of Sam’s savings to Ray’s savings was 5:4. After each of them donated $45 to charity, the ratio of Sam’s savings to Ray’s savings became 13:10. What was Sam’s savings at first?

Example: Dan had 50% fewer stickers than Jeff. After Jeff gave 20 of his stickers to Dan, Dan had 40% fewer stickers than Jeff (had after he gave away 20 of his stickers). How many stickers did Dan have at first?

Example: There are 8 more girls than boys in a particular class. 3/5 of the boys and 1/3 of the girls were born in Georgia. If the number of boys that were born in Georgia is equal to the number of girls that were born in Georgia, how many students (boys and girls together) in that class were born in Georgia?

Example: Ray and Omar collect stamps. Originally, 1/5 of Omar’s stamps were equivalent to 1/3 of Ray’s stamps. If Ray gave Omar 24 stamps, Omar would have 3 times as many stamps as Ray. Find the number of stamps each of them had in the beginning.

Example: Jim had 103 red and blue marbles. After giving 2/5 of his blue marbles and 15 of his red marbles to Samantha, Jim had 3/7 as many red marbles as blue marbles. How many blue marbles did he have originally?

Example: The ratio of the amount of turkey to the amount of chicken at the grocery store was 8:3 in the morning. By the end of the day, 14 pounds of turkey had been sold. The ratio of the amount of turkey to the amount of chicken was now 3:2. a. How many pounds of turkey did the grocery store have in the morning? b. How many pounds of chicken did the grocery store have in the morning?

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7th Grade Mathematics Worksheets: FREE & Printable

Looking for FREE printable 7th-grade math questions and exercises to help your students review and practice 7th-grade mathematics concepts?

Need Mathematics Practice questions to measure your 7th-grade student’s exam readiness? If so, then look no further.

Here is a comprehensive collection of free exercises and worksheets that would help your students for 7th Grade Math preparation and practice.

Download our free Mathematics worksheets for the 7th Grade Math.

You can download free 50+ 7th Grade Math Worksheets  from Bytelearn.

Hope you enjoy it!

IMPORTANT: COPYRIGHT TERMS: These worksheets are for personal use. Worksheets may not be uploaded to the internet, including classroom/personal websites or network drives. You can download the worksheets and print as many as you need. You can distribute the printed copies to your students, teachers, tutors, and friends. 

You Do NOT have permission to send these worksheets to anyone in any way (via email, text messages, or other ways). They MUST download the worksheets themselves. You can send the address of this page to your students, tutors, friends, etc.

Related Topics

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The Absolute Best Workbook to Review 7th-Grade Math Concepts!

Mastering Grade 8 Math The Ultimate Step by Step Guide to Acing 8th Grade Math

7th grade mathematics concepts, fractions and decimals.

• Simplifying Fractions
• Adding and Subtracting Fractions
• Multiplying and Dividing Fractions
• Adding and Subtracting Mixed Numbers
• Multiplying and Dividing Mixed Numbers
• Adding and Subtracting Decimals
• Multiplying and Dividing Decimals
• Comparing Decimals
• Rounding Decimals
• Factoring Numbers
• Greatest Common Factor
• Least Common Multiple

Real Numbers and Integers

• Adding and Subtracting Integers
• Multiplying and Dividing Integers
• Order of Operations
• Ordering Integers and Numbers
• Integers and Absolute Value

Proportions, Ratios, and Percent

• Simplifying Ratios
• Proportional Ratios
• Similarity and Ratios
• Ratio and Rates Word Problems
• Percentage Calculations
• Percent Problems
• Discount, Tax and Tip
• Percent of Change
• Simple Interest

Algebraic Expressions

• Simplifying Variable Expressions
• Simplifying Polynomial Expressions
• Translate Phrases into an Algebraic Statement
• The Distributive Property
• Evaluating One Variable Expressions
• Evaluating Two Variables Expressions
• Combining like Terms

Equations and Inequalities

• One-Step Equations
• Multi-Step Equations
• Graphing Single–Variable Inequalities
• One-Step Inequalities
• Multi-Step Inequalities

Systems of Equations

• Systems of Equations Word Problems
• Quadratic Equation

Linear Functions

• Finding Slope
• Graphing Lines Using Line Equation
• Writing Linear Equations
• Graphing Linear Inequalities

Exponents and Radicals

• Multiplication Property of Exponents
• Zero and Negative Exponents
• Division Property of Exponents
• Powers of Products and Quotients
• Negative Exponents and Negative Bases
• Scientific Notation
• Square Roots

Geometry and Solid Figures

• Pythagorean Relationship
• Rectangular Prism
• Pyramids and Cone

Statistics and Probability

• Mean and Median
• Mode and Range
• Stem–and–Leaf Plot
• Probability Problems
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The Best Book to Ace 7th-Grade Math Concepts!

Mastering Grade 8 Math Word Problems The Ultimate Guide to Tackling 8th Grade Math Word Problems

7th grade math exercises, proportions and ratios, polynomials, solid figures.

Looking for the best resources to help your students review and practice Math topics?

The Best Books to Ace the Math Test!

Mastering Grade 6 Math Word Problems The Ultimate Guide to Tackling 6th Grade Math Word Problems

Mastering grade 5 math word problems the ultimate guide to tackling 5th grade math word problems, mastering grade 7 math word problems the ultimate guide to tackling 7th grade math word problems.

by: Effortless Math Team about 4 years ago (category: Blog , Free Math Worksheets )

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Building Problem-solving Skills for 7th-Grade Math

Mathematics is a subject that requires problem-solving skills to excel. In 7th grade, students begin to encounter more complex math concepts, and the ability to analyze and solve problems becomes increasingly important. Building problem-solving skills for math not only helps students to master math concepts but also prepares them for success in higher-level math courses and in life beyond academics. 

In this article, we will several key skills that are needed for success in 7th-grade math, and also explore how they can benefit students both academically and personally. We will also provide tips and strategies to help students develop and improve their problem-solving skills. Let’s dive in!

Building Analytical Skills

The first of seven important skills to build is that of analytical skills. These allow students to analyze a problem and break it down into smaller parts. From there, they’re able to identify the key components that need to be addressed. Analytical skills also hone students’ abilities to identify patterns. Students should be able to identify patterns in mathematical data, such as in number sequences, geometric shapes, and graphs. Importantly, students should not just be able to recognize the pattens, but they should be able to describe them (more on that in communication) and use them to make predictions and solve problems.

We alluded to this earlier, but breaking down problems is an essential component of analytical skills. Students with strong analytical skills can break problems down into smaller and more manageable parts. They are then able to identify key components of a problem and use this information to develop a strategy for solving it. 

Along with identifying patterns comes identifying relationships. Students with good mathematical analytical skills can identify relationships between different mathematical concepts, such as the relationship between addition and subtraction, or the relationship between angles and shapes. Through strengthening this skill, students will be able to describe these relationships and use them to solve problems. 

An important part of analytical skills is the ability to analyze data. Students should be able to analyzeand interpret data presented in a variety of formats, such as graphs, charts, and tables. They should be able to use this data to make predictions, draw conclusions, and solve problems.

Speaking of conclusions, reaching sound conclusions based on mathematical data is a fundamental skill needed for making predictions based on trends in a graph, or drawing inferences from a set of data.

Another skill students should master is the ability to compare and contrast mathematical concepts, such as the properties of different shapes or the strategies for solving different types of problems. Through this, they’ll be able to use the information they gather to solve problems. 

With all these skills at play comes arguably the most important: Critical thinking. This is an indicator that a student really grasps the concepts and it’s just repeating them back to you on command. Critical thinking is the ability to evaluate information and arguments, and make judgements and decisions based on evidence, and apply logic and reasoning to solve problems.

Building Creative Thinking

This is the ability for students (or anyone, really) to think outside the box and come up with innovative solutions to problems. This involves being able to approach problems from different angles and to consider multiple perspectives. For a 7th-grader, this skill can be exercised through the following:

• Thinking Outside the Box: Students should be encouraged to think creatively and come up with innovative solutions to problems. This involves thinking outside the box and considering multiple perspectives.
• Finding Multiple Solutions: Students should be able to come up with multiple solutions to a problem and evaluate each one to determine which is the most effective.
• Developing Original Ideas: Students should be able to develop original ideas and approaches to solving problems. This involves being able to come up with unique and innovative solutions that may not have been tried before.
• Making Connections: Students should be able to make connections between different mathematical concepts and apply these connections to solve problems. This involves looking for similarities and differences between concepts and using this information to make new connections.
• Visualizing Solutions : Students should be able to visualize solutions to problems and use diagrams, charts, and other visual aids to help them solve problems.
• Using Metaphors and Analogies: Students should be able to use metaphors and analogies to help them understand complex mathematical concepts. This involves using familiar concepts to explain unfamiliar ones and making connections between different ideas.

Building Problem-Solving Strategies

It may sound like the same thing, but building problem-solving strategies is not the same as building problem-solving skills. Building strategies for problem-solving lends itself to actual problem-solving. Let’s expand on this: Say your student is presented a problem that they’re struggling with, these are some of the problem-solving strategies they may use in order to solve the puzzle.

• Identify the problem: The first step in problem-solving is to identify the problem and understand what is being asked. Students should carefully read the problem and make sure they understand the question before attempting to solve it.
• Draw a diagram: Students can draw a diagram to help visualize the problem and better understand the relationships between different parts of the problem.
• Use logic: Students can use logic to identify patterns and relationships in the problem. They can use this information to develop a plan to solve the problem.
• Break the problem down: Students can break a complex problem down into smaller, more manageable parts. They can then solve each part of the problem individually before combining the solutions to get the final answer.
• Guess and check: Students can guess and check different solutions to the problem until they find the correct answer. This method involves trying different solutions and evaluating the results until the correct answer is found.
• Use algebra: Algebraic equations can be used to solve a variety of mathematical problems. Students can use algebraic equations to represent the problem and solve for the unknown variable.
• Work backward: Students can work backward from the final answer to determine the steps required to solve the problem. This method involves starting with the end goal and working backward to determine the steps needed to get there.

Building Persistence and Perseverance

In an increasingly instant-gratification world with apps, searches and AI chatbots just a click away, this is an important skill not just in the math classroom, but for life in general. Problem-solving, whether that’s a math problem or a life challenge, often requires persistence and perseverance. Student need to learn to be able to stick with a problem even when it seems challenging, difficult, or seemingly impossible. Here are ways you can encourage your students to stick it out when working on problems:

• Trying multiple approaches: When faced with a challenging problem, students can demonstrate persistence by trying multiple approaches until they find one that works. They don’t give up after one attempt but keep trying until they find a solution.
• Reframing the problem: If a problem seems particularly difficult, students can demonstrate perseverance by reframing the problem in a different way. This can help them see the problem from a new perspective and come up with a different approach to solve it.
• Asking for help: Sometimes, even with persistence, a problem may still be difficult to solve. In these cases, students can demonstrate perseverance by asking for help from their teacher or classmates. This shows that they are willing to put in the effort to find a solution, even if it means seeking assistance.
• Learning from mistakes: Making mistakes is a natural part of the problem-solving process, but students can demonstrate persistence by learning from their mistakes and using them to improve their problem-solving skills. They don’t get discouraged by their mistakes, but instead, they use them as an opportunity to learn and grow.
• Staying focused: In order to solve complex math problems, it’s important for students to stay focused and avoid distractions. Students can demonstrate perseverance by staying focused on the problem at hand and not getting distracted by other things.

Building Communication Skills

We alluded to this earlier, but a central part of building problem-solving skills is building the ability to articulate a problem or a solution. This isn’t just for the sake of personal understanding, but critical for collaboration. Students need to be able to explain their thinking, ask questions, and work with others to solve problems. Here are some examples of communication skills that can be used to build problem-solving skills:

• Clarifying understanding: Students can ask questions to clarify their understanding of the problem. They can seek clarification from their teacher or classmates to ensure they are interpreting the problem correctly.
• Explaining their reasoning: When solving a math problem, students can explain their reasoning to show how they arrived at a particular solution. This can help others understand their thought process and can also help students identify errors in their own work.
• Collaborating with peers: Problem-solving can be a collaborative effort. Students can work together in groups to solve problems and communicate their ideas and solutions with each other. This can lead to a better understanding of the problem and can also help students learn from each other.
• Writing clear explanations: When presenting their solutions to a math problem, students can write clear and concise explanations that are easy to understand. This can help others follow their thought process and can also help them communicate their ideas more effectively.
• Using math vocabulary: Math has its own language and using math vocabulary correctly is essential for effective communication. Students can demonstrate their understanding of math concepts by using correct mathematical terms and symbols when explaining their solutions.

Building Mathematical Knowledge

This would seem like a no-brainer, since you’re a math educator clicking on an article about building math problem-solving skills. However, it’s worth being explicit that problem-solving in math requires a solid understanding of mathematical concepts, including arithmetic, algebra, geometry, and data analysis. Students need to be able to apply these concepts to solve problems in real-world contexts.

7th-grade math covers a wide range of mathematical concepts and skills. Here are some examples of mathematical knowledge that 7th-grade math students should have:

• Algebraic expressions and equations: Students should be able to write and simplify algebraic expressions and solve one-step and two-step equations.
• Proportional relationships: Students should be able to understand and apply proportional relationships, including identifying proportional relationships in tables, graphs, and equations.
• Geometry: Students should have a solid understanding of geometry concepts such as angles, triangles, quadrilaterals, circles, and transformations.
• Statistics and probability: Students should be able to analyze and interpret data using measures of central tendency and variability, and understand basic probability concepts.
• Rational numbers: Students should have a solid understanding of rational numbers, including ordering, adding, subtracting, multiplying, and dividing fractions and decimals.
• Integers: Students should be able to perform operations with integers, including adding, subtracting, multiplying, and dividing.
• Ratios and proportions: Students should be able to understand and use ratios and proportions in a variety of contexts, including scale drawings and maps.

In conclusion, problem-solving skills are essential for success in 7th grade math. Analytical skills, critical and creative thinking, problem-solving strategies, persistence, communication skills, and mathematical knowledge are all important components of effective problem-solving. By developing these skills, students can approach math problems with confidence and achieve their full potential.

If you enjoyed this read, be sure to browse more of our articles . More importantly, if you want to save yourself hours of preparation time by having full math curriculums, review guides and tests available at the click of a button, be sure to sign up to our 7th Grade Newsletter . You’ll receive loads of free lesson resources, tips and advice and exclusive subscription offers!

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Build Confidence with Math Problem Solving

Daily Problem Solving will help your 7th grade students master the skills they need to be successful with challenging word problems...and have fun doing it .

What you'll get with this download:

Your download includes a full week of Daily Problem Solving for Grade 7 to try out in your own classroom. Developed with the brain in mind, these multi-step word problems will challenge your learners without overwhelming them. Best of all, you'll be able to watch their skills and confidence grow as they begin to internalize strategies for conquering this difficult math skill.

FUN & ENGAGING

Themed-problems and a weekly fun fact make it easy to keep learners engaged

MINIMAL PREP

Formatted for quick & easy implementation that won't add stress to your planning

PRINT & DIGITAL

Includes both print and digital student options for added flexibility

I've been using this with my extremely anxious learner and it works wonders to build confidence because we see the improvement.

These have given me such an insight into my students' abilities, and I've watched them improve their skills and successfully solve multi-step word problems.

Jilliana D.

STUDENT PRINTABLES

You'll receive a full week of printable Daily Problem Solving practice for your students. This format includes:

• Paper-saving format that fits a full week on one page
• Space for student work, feedback, and self-reflection
• Themed problems & weekly fun fact to engage

DIGITAL SLIDES

Daily digital slides offer your remote or online learners the opportunity to build problem-solving skills in a structured format designed for success.

• Single slide per day prevents overwhelm or distraction
• Organized with clear space to solve & answer
• Engaging graphics, themed problems, & fun facts

Don’t wait, get started helping your learners master word problems today!

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Unit 2: Rates and percentages

About this unit.

In these tutorials, we'll look at how rates and percentages relate to proportional thinking. We'll also solve interesting word problems involving percentages (discounts, taxes, and tip calculations).

Rate problems with fractions

• Fractions, decimals, & percentages FAQ (Opens a modal)
• Rates with fractions (Opens a modal)
• Rates with fractions Get 3 of 4 questions to level up!

Converting fractions to decimals

• Rewriting decimals as fractions: 2.75 (Opens a modal)
• Worked example: Converting a fraction (7/8) to a decimal (Opens a modal)
• Fraction to decimal: 11/25 (Opens a modal)
• Fraction to decimal with rounding (Opens a modal)
• Comparing rational numbers (Opens a modal)
• Rewriting decimals as fractions challenge Get 5 of 7 questions to level up!
• Converting fractions to decimals Get 3 of 4 questions to level up!
• Order rational numbers Get 3 of 4 questions to level up!

Percent word problems

• Solving percent problems (Opens a modal)
• Percent word problem: magic club (Opens a modal)
• Percent word problems: tax and discount (Opens a modal)
• Percent word problem: guavas (Opens a modal)
• Multi-step ratio and percent problems (Opens a modal)
• Equivalent expressions with percent problems Get 3 of 4 questions to level up!
• Percent problems Get 3 of 4 questions to level up!
• Tax and tip word problems Get 3 of 4 questions to level up!
• Discount, markup, and commission word problems Get 3 of 4 questions to level up!

7th Grade Math Problems

In 7th grade math problems you will get all types of examples on different topics along with the solutions.

Keeping in mind the mental level of child in Grade 7, every efforts has been made to introduce new concepts in a simple language, so that the child understands them easily. The difficulty level of the problems has been reduced and mathematical concepts have been explained in the simplest possible way. Each topic contains a large number of examples to understand the applications of concepts. If student follow math-only-math they can improve their knowledge by practicing the solutions step by step which will help you to score in your exam.

●  Set Theory

Sets : An introduction to sets, methods for defining sets, element of set and use of set notations.

Objects Form a Set : State, whether the following objects form a set or not by giving reasons.

Elements of a Set : Learn how to find the elements of a set with the help of various types of problems on the basic concepts of sets.

Properties of Sets : Using the basic properties to represent a set learn to solve various basic types of problems on sets.

Representation of a Set : Definition with examples of statement form, roster form or tabular form, set builder form cardinal number of a set and the standard sets of numbers.

Different Notations in Sets : Some of the familiar notations used in sets which are generally required to solve various types of problems on sets.

Standard Sets of Numbers : Learn to represent the standard sets of numbers using the three methods i.e. statement form, roster form and set builder form.

Types of Sets : Definition with examples of empty set or null set, singleton set, finite set, infinite set, cardinal number of a set, equivalent set and equal sets.

Pairs of Sets : Definition with examples of equal set, equivalent set, disjoint sets and overlapping set.

Subset : Definition with examples of subset and its types, super set, proper subset, power set and universal set.

Subsets of a Given Set : How to find the number of subsets of a given set and number of proper subsets of a given set.

Operations on Sets : Learn the meaning. What are the four basic operations on sets? How the operations are carried out in union of sets and intersection of sets?

Union of Sets : Definition of union of sets with examples. Learn how to find the union of two sets and worked-out examples.

Intersection of Sets : Definition of intersection of sets with examples. Learn how to find the intersection of two sets and worked-out examples.

Difference of two Sets : Learn how to find the difference between the two sets and worked-out examples.

Complement of a Set : Definition of complement of a set and their properties with some worked-out examples.

Cardinal number of a set : Definition of a cardinal number of a set, the symbol used for showing the cardinal number, worked-out examples.

Cardinal Properties of Sets : Learn how to solve the real-life word problems on set using the cardinal properties.

Venn Diagrams : Learn to represent the basic concepts of sets using Venn-diagram in different situations.

● Relations and Mapping

Ordered Pair

Cartesian Product of Two Sets

Domain and Range of a Relation

Functions or Mapping

Domain Co-domain and Range of Function

● Relations and Mapping - Worksheets

Worksheet on Math Relation

Worksheet on Functions or Mapping

● Numbers - Integers

Multiplication of Integers

Properties of Multiplication of Integers

Examples on Multiplication of Integers

Division of Integers

Absolute Value of an Integer

Comparison of Integers

Properties of Division of Integers

Examples on Division of Integers

Fundamental Operation

Examples on Fundamental Operations

Uses of Brackets

Removal of Brackets

Examples on Simplification

● Numbers - Worksheets

Worksheet on Multiplication of Integers

Worksheet on Division of Integers

Worksheet on Fundamental Operation

Worksheet on Simplification

● Fractions

Types of Fractions

Equivalent Fractions

Like and Unlike Fractions

Conversion of Fractions

Fraction in Lowest Terms

Addition and Subtraction of Fractions

Multiplication of Fractions

Division of Fractions

● Fractions - Worksheets

Worksheet on Fractions

Worksheet on Multiplication of Fractions

Worksheet on Division of Fractions

● Story about the Decimal Number

Decimals : Concept for decimals in derails.

Decimal Numbers : Learn reading decimal numbers, writing decimal numbers etc,.

Decimal Fractions : Learn reading decimal fractions, writing decimal fractions.

Decimal Places : Learn reading and writing the place values of a decimal number in words.

Decimal and Fractional Expansion : Learn how to expand the decimal numbers and the decimal numbers in fractions

Like and Unlike Decimals : Learn to identify like decimals and unlike decimals.

Conversion of Unlike Decimals to Like Decimals : Learn to convert unlike decimals in like decimals

Comparing Decimals : Learn to order and compare decimal numbers, arranging decimals in ascending order and arranging decimals in descending order

Adding Decimals : Learn to add decimals in the correct order, word problems.

Subtracting Decimals : Learn to subtract decimals in the correct order, word problems

Simplify Decimals Involving Addition and Subtraction Decimals : Examples for simplifying decimals for adding and subtracting.

Multiplying Decimal by a Whole Number : Learn to multiply decimals by a whole number in the correct order, word problems

Multiplying Decimal by a Decimal Number : Learn to multiply decimals by a decimal number in the correct order, word problems

Dividing Decimal by a Whole Number : Learn to divide decimals by a whole number in the correct order, word problems

Dividing Decimal by a Decimal Number : Learn to divide decimals by a decimal number in the correct order, word problems

Simplification of Decimal : Examples for simplifying decimals, operation on decimals.

Converting Decimals to Fractions : Learn to express decimal number into fraction

Converting Fractions to Decimals : Learn to express fraction into decimal number

Rounding Decimals : Learn to round off decimals

Rounding Decimals to the Nearest Whole Number : Learn to round off decimals to the nearest whole number

Rounding Decimals to the Nearest Tenths : Learn to round off decimals to the nearest tenths

Rounding Decimals to the Nearest Hundredths : Learn to round off decimals to the nearest hundredths

Round a Decimal : Problems for rounding off decimals

H.C.F. and L.C.M. of Decimals : Learn to find the highest common factor, lowest common multiple of more than two decimal numbers

Terminating Decimal : Definition of terminating decimals, examples to identify terminating decimals

Non-Terminating Decimal : Definition of non-terminating decimal, examples to identify non-terminating decimals

Repeating or Recurring Decimal : Definition of recurring decimals, examples to identify recurring decimals

Pure Recurring Decimal : Definition of pure recurring decimal, examples to pure recurring decimal

Mixed Recurring Decimal : Definition of mixed recurring decimal, examples to identify mixed recurring decimal

Conversion of Pure Recurring Decimal into Vulgar Fraction : Learn to express pure recurring decimals to vulgar fractions with examples.

Conversion of Mixed Recurring Decimals into Vulgar Fractions : Learn to express mixed recurring decimals to vulgar fractions with examples.

BODMAS/PEMDAS rule:

BODMAS Rule : Learn how to follow the BODMAS rules to simply the order of operations.

BODMAS Rules - Involving Integers : Learn how to follow the BODMAS rules to simply the order of operations involving integers.

BODMAS/PEMDAS Rules - Involving Decimals : Learn how to follow the BODMAS rules to simply the order of operations involving decimals

PEMDAS Rule : Learn how to follow the PEMDAS rules to simply the order of operations.

PEMDAS Rules - Involving Integers : Learn how to follow the PEMDAS rules to simply the order of operations involving integers.

PEMDAS Rules - Involving Decimals : Learn how to follow the PEMDAS rules to simply the order of operations involving decimals.

● Profit, Loss and Discount

Concept of Profit and Loss

Calculate Profit and Profit Percent

Calculate Loss and Loss Percent

Calculate Cost Price using Sell Price and Loss Percent

Calculate Cost Price using Sell Price and Profit Percent

Calculate Selling Price using Cost and Loss Percent

Calculate Selling Price using Cost and Profit Percent

Calculating Profit Percent and Loss Percent

Word Problems on Profit and Loss

Examples on Calculating Profit or Loss

Practice Test on Profit and Loss

Practice Test on Profit Loss and Discount

● Profit, Loss and Discount - Worksheets

Worksheet to Find Profit and Loss

Worksheets on Profit and Loss Percentage

Worksheet on Gain and Loss Percentage

Worksheet on Discounts

● Ratios and Proportions

What is a Ratio?

What is a Proportion?

● Ratios and Proportions - Worksheets

Worksheet on Ratios

Worksheet on Proportions

● Time and Work

Calculate Time to Complete a Work

Calculate Work Done in a Given Time

Problems on Time required to Complete a Piece a Work

Problems on Work Done in a Given Period of Time

Problems on Time and Work

Pipes and Water Tank

Problems on Pipes and Water Tank

● Time and Work - Worksheets

Worksheet on Work Done in a Given Period of Time

Worksheet on Time Required to Complete a Piece of Work

Worksheet on Pipes and Water Tank

● Unitary Method

Problems Using Unitary Method

Situations of Direct Variation

Situations of Inverse Variation

Direct Variations Using Unitary Method

Direct Variations Using Method of Proportion

Inverse Variation Using Unitary Method

Inverse Variation Using Method of Proportion

Problems on Unitary Method using Direct Variation

Problems on Unitary Method Using Inverse Variation

Mixed Problems Using Unitary Method

● Unitary Method - Worksheets

Worksheet on Direct Variation using Unitary Method

Worksheet on Direct variation using Method of Proportion

Worksheet on Word Problems on Unitary Method

Worksheet on Inverse Variation Using Unitary Method

Worksheet on Inverse Variation Using Method of Proportion

● Simple Interest

What is Simple Interest?

Calculate Simple Interest

Practice Test on Simple Interest

● Simple Interest - Worksheets

Simple Interest Worksheet

● Algebraic Expressions

Division of Polynomial by Monomial

● Algebraic Expressions - Worksheets

Worksheet on Dividing Polynomial by Monomial

Formula and Framing the Formula

Change the Subject of a Formula

Changing the Subject in an Equation or Formula

Practice Test on Framing the Formula

● Formula - Worksheets

Worksheet on Framing the Formula

Worksheet on Changing the Subject of a Formula

Worksheet on Changing the Subject in an Equation or Formula

● Algebraic Identities

Square of The Sum of Two Binomials : Using the formula of (a + b) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + 2ab, learn to evaluate the square of the sum of two terms.

Square of The Difference of Two Binomials : Using the formula of (a - b)\(^{2}\)  = a \(^{2}\) + b \(^{2}\) - 2ab, learn to evaluate the square of the difference of two terms.

Product of Sum and Difference of Two Binomials : Using the formula of a \(^{2}\) - b \(^{2}\) = (a + b) (a - b), learn to evaluate the product of sum and difference of two terms.

Product of Two Binomials whose First Terms are Same and Second Terms are Different : Learn to use the given formulas to evaluate the product of the two terms whose 1 \(^{st}\) terms are same and 2 \(^{nd}\) terms are different.

• (x + a) (x + b) = x \(^{2}\) + x(a + b) + ab

• (x + a) (x - b) = x \(^{2}\) + x (a – b) – ab

• (x - a) (x - b) = x \(^{2}\) – x (a + b) + ab

• (x - a) (x + b) = x \(^{2}\) + x (b – a) – ab

Square of a Trinomial : Learn to use the formula for the expansion of the square of a trinomial.

• (a + b + c) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + c \(^{2}\) + 2ab + 2bc + 2ca

• (a + b - c) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + c \(^{2}\) + 2ab – 2bc - 2ca

• (a - b + c) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + c \(^{2}\) – 2ab – 2bc + 2ca

• (a - b - c) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + c \(^{2}\) – 2ab + 2bc – 2ca

Cube of The Sum of Two Binomials : Learn the formula to determine the cube of the sum of two terms.

(a + b) \(^{3}\) = a \(^{3}\)   + 3a \(^{2}\) b + 3ab \(^{2}\)   + b \(^{3}\)

             = a \(^{3}\) + b \(^{3}\) + 3ab (a + b)

Cube of The Difference of Two Binomials : Learn the formula to determine the cube of the difference of two terms.

(a - b) \(^{3}\) = a \(^{3}\)   – 3a \(^{2}\) b + 3ab \(^{2}\)   – b \(^{3}\)

           = a \(^{3}\) – b \(^{3}\) – 3ab (a - b)

Cube of a Binomial :

Square of a Binomial :

● Equations

What is an Equation?

What is a Linear Equation?

How to Solve Linear Equations?

Solving Linear Equations

Problems on Linear Equations in One Variable

Word Problems on Linear Equations in One Variable

Practice Test on Linear Equations

Practice Test on Word Problems on Linear Equations

● Equations - Worksheets

Worksheet on Linear Equations

Worksheet on Word Problems on Linear Equation

● Inequations

What are Linear Inequality?

What are Linear Inequations?

Properties of Inequation or Inequalities

Representation of the Solution Set of an Inequation

Practice Test on Linear Inequation

● Inequations - Worksheets

Worksheet on Linear Inequations

● Lines and Angles

Fundamental Geometrical Concepts

Classification of Angles

Related Angles

Some Geometric Terms and Results

Complementary Angles

Supplementary Angles

Complementary and Supplementary Angles

Adjacent Angles

Linear Pair of Angles

Vertically Opposite Angles

Parallel Lines

Transversal Line

Parallel and Transversal Lines

● Congruence

Congruent Shapes :

Congruent Line-segments :

Congruent Angles :

Congruent Triangles :

Conditions for the Congruence of Triangles :

Side Side Side Congruence :

Side Angle Side Congruence : 

Angle Side Angle Congruence :

Angle Angle Side Congruence :

Right Angle Hypotenuse Side congruence :

Pythagorean Theorem :

Proof of Pythagorean Theorem :

Converse of Pythagorean Theorem :

Word problems on Pythagorean Theorem :

Polygon and its Classification

Terms Related to Polygons

Interior and Exterior of the Polygon

Convex and Concave Polygons

Regular and Irregular Polygon

Number of Triangles Contained in a Polygon

Angle Sum Property of a Polygon

Problems on Angle Sum Property of a Polygon

Sum of the Interior Angles of a Polygon

Sum of the Exterior Angles of a Polygon

● Polygons - Worksheets

Worksheet on Polygon and its Classification

Worksheet on Interior Angles of a Polygon

Worksheet on Exterior Angles of a Polygon

● Quadrilateral

Quadrilateral : Perimeter of Quadrilateral : Angle Sum Property of a Quadrilateral : Missing angle of a Quadrilateral :

Angles of a Quadrilateral are in Ratio :

●   Symmetrical Figure

Linear Symmetry :  Identify symmetric and non-symmetric figures and also identify shapes having horizontal line of symmetry, vertical line of symmetry, both horizontal and vertical lines of symmetry, infinite lines of symmetry and no line of symmetry.

Lines of Symmetry :  Identify the geometrical shapes having 1, 2, 3, 4, 0 and so on or infinite lines of symmetry.

Point Symmetry :  How to find the point symmetry of letters of the English alphabet and the different geometrical figures. Learn the important points to find the conditions that satisfy centre of symmetry.

Reflection Symmetry :

Nets of a Solids :

Rotational Symmetry :  Learn what is rotational symmetry and types of rotation i.e. clockwise rotation and anticlockwise rotation. 

Order of Rotational Symmetry :  Learn the different orders of rotation of the shapes through 360° in clockwise direction and anticlockwise direction.

Types of Symmetry :  Learn the various symmetries i.e. linear symmetry, point symmetry and rotational symmetry of the geometrical shapes. 

Reflection :  Learn how reflection is related to math, define reflection using an image and worked-out examples on math reflection. 

Reflection of a Point in x-axis :  Learn how to draw the image on the graph paper to find the reflection of a point in x-axis.

Reflection of a Point in y-axis :  Learn how to draw the image on the graph paper to find the reflection of a point in y-axis.

Reflection of a point in origin :  Learn how to draw the image on the graph paper to find the reflection of a point in origin. 

Rotation :  Explanation of rotation using an image.

90 Degree Clockwise Rotation :  Learn with the help of solved examples to rotate a figure 90 degrees clockwise direction around the origin on a graph paper.

90 Degree Anticlockwise Rotation :  Learn with the help of solved examples to rotate a figure 90 degrees anticlockwise direction around the origin on a graph paper.

180 Degree Rotation :  Learn with the help of solved examples to rotate a figure 180 degrees clockwise direction and anticlockwise direction around the origin on a graph paper.

●  Coordinate System

• Coordinate Graph
• Ordered pair of a Coordinate System
• Plot Ordered Pairs
• Coordinates of a Point
• All Four Quadrants
• Signs of Coordinates
• Find the Coordinates of a Point
• Coordinates of a Point in a Plane
• Plot Points on Coordinate Graph
• Graph of Linear Equation
• Simultaneous Equations Graphically
• Graphs of Simple Function
• Graph of Perimeter vs. Length of the Side of a Square
• Graph of Area vs. Side of a Square
• Graph of Simple Interest vs. Number of Years
• Graph of Distance vs. Time

●  Mensuration

• Area and Perimeter
• Perimeter and Area of Rectangle
• Perimeter and Area of Square
• Area of the Path
• Area and Perimeter of the Triangle
• Area and Perimeter of the Parallelogram
• Area and Perimeter of Rhombus
• Area of Trapezium
• Circumference and Area of Circle
• Units of Area Conversion
• Practice Test on Area and Perimeter of Rectangle
• Practice Test on Area and Perimeter of Square

●  Mensuration - Worksheets

• Worksheet on Area and Perimeter of Rectangles
• Worksheet on Area and Perimeter of Squares
• Worksheet on Area of the Path
• Worksheet on Circumference and Area of Circle
• Worksheet on Area and Perimeter of Triangle

●   Volume and Surface Area of Solids

• Volume of Cubes and Cuboids
• Worked-out Problems on Volume of a Cuboid

●  Statistics

• Real Life Statistics
• Terms Related to Statistics
• Frequency Distribution of Ungrouped and Grouped Data
• Use of Tally Marks
• Class Limits in Exclusive and Inclusive Form
• Construction of Bar Graphs
• Mean of the Tabulated Data
• Construction of Pie Chart
• How to Construct a Line Graph?

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• 7th Grade Mathematics
• Problem-Solving

Education Standards

Maryland college and career ready math standards.

Learning Domain: Expressions and Equations

Standard: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Standard: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Standard: Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Learning Domain: Geometry

Standard: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Common Core State Standards Math

Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Refining Problem Solving Skills

Students critique the diagrams of other students from the previous lesson and receive feedback about their own diagrams. Students revise their diagrams from the first part of the lesson based on the feedback they receive.

Key Concepts

Students are expected to use the mathematical skills they have acquired in previous lessons or in previous math courses. The lessons in this unit focus on developing and refining problem-solving skills. Students will:

• Try a variety of strategies to approaching different types of problems.
• Devise a problem-solving plan and implement their plan systematically.
• Become aware that problems can be solved in more than one way.
• See the value of approaching problems in a systematic manner.
• Communicate their approaches with precision and articulate why their strategies and solutions are reasonable.
• Make connections between previous learning and real-world problems.
• Create efficacy and confidence in solving challenging problems in a real-world setting.

Goals and Learning Objectives

• Read and interpret maps, graphs, and diagrams.
• Solve problems that involve linear measurement.
• Estimate length.
• Critique a diagram.

SWD: Some students with disabilities will benefit from a preview of the goals in each lesson. Students can highlight the critical features and/or concepts and will help them to pay close attention to salient information. Students need to know their goal is to develop and refine their problem solving skills.

Math Mission

Lesson guide.

Discuss the Math Mission. Students will critique their classmates' diagrams of a ship's journey through the Welland Canal and revise their own diagram.

SWD: Model for students how to give constructive feedback to their peers. They should comment on one thing that their peer did well and one specific area that could be improved. Remind them to be specific, objective, and kind with their comments.

Critique diagrams of a ship’s journey through the Welland Canal, and revise your own diagram.

Critique and Revise

Begin the lesson by asking students:

What do you think is a strong point of your diagram?

Give students an opportunity to share a strong point of their diagram with their partner. Have partners trade diagrams with another pair of students and critique their diagrams. Students should analyze the diagrams for clarity, reasonableness, and accuracy.

Guide students to ask themselves the following questions as they critique the diagrams:

• Is the diagram understandable?
• Are there ways the diagram could show the information more clearly?
• Is there anything in the diagram that is not correct?

After students have critiqued the diagrams, have them refine their own diagrams independently based on the critique of others. While students are critiquing and revising their diagrams, circulate around the room asking guiding questions and looking for strategies and thought processes to highlight during the class discussion.

ELL: Show these questions in writing and provide sentence frames to support ELLs such as the following:

Post these sentence frames as a reference for future lessons.

• “I think the results were....(very, somewhat, relatively, extremely)....accurate because....”
• “The image on the screen is different/similar from the actual drawing or model in that.....”
• “It shows...”
• “This diagram makes sense to me because.....”
• “The structure of the mathematics was brought up by.....”

Mathematical Practices

Mathematical Practice 3: Construct viable arguments and critique the reasoning of others.

• Students provide focused, specific critiques on diagrams created by their classmates to help them refine their work.

Mathematical Practice 4: Model with mathematics.

• Students model the mathematics through the creation of their diagrams.

Mathematical Practice 6: Attend to precision.

• Students attend to precision while refining their diagrams ensuring that their revisions depict the correct data in a way that others can comprehend.

Interventions

Student has difficulty getting started.

• What are the strengths and weaknesses of the diagram you are critiquing?
• How can you improve upon your diagram?
• What items are essential in every diagram?

Student has an answer, but it is incorrect.

• Does your diagram depict the correct information?
• Can others understand your diagram?

Student has an answer but is having difficulty articulating their reasoning.

• How did you improve upon your diagram?
• How did the critique of your diagram help guide your thinking when revising it?
• What were some mistakes you found in your diagram?

Student has the correct answer and is waiting on others to finish.

• What other diagrams can you create to show the journey through the canal?
• Compare and contrast your diagram to the diagram shown on the tablet. How do they compare?

Possible Answers

• Answers will vary.

Trade diagrams and critique each other’s work. Use the following questions to help guide your critique of another student's work.

• Are there ways that the diagram could show the information more clearly?

Diagram of Welland Canal

Guide students to ask themselves the following questions as they critique the diagram:

• Answers will vary. Possible answer: The diagram shows the vertical distance gained and the horizontal distance traveled for a ship traveling from Lake Ontario to Lake Erie through the locks along the Welland Canal.

When you have finished critiquing your partner’s diagram, look at this diagram of the Welland Canal.

• What does the diagram show?
• Critique the diagram.
• What does the title of the given diagram tell you?
• What do the numbers along the vertical axis represent?
• What do the numbers along the horizontal axis represent?

Revise Your Work

After students have critiqued the diagrams, have them refine their own diagrams independently based on the critique of others.

While students are critiquing and revising their diagrams, circulate around the room asking guiding questions and looking for strategies and thought processes to highlight during the class discussion.

ELL: For this task, encourage students to explain their ideas to one another. Math language must be used. Encourage the use of English without discouraging students from using their first language(s). Students may have questions when they are making revisions for their diagrams. Make sure students are expressing the horizontal and vertical distances accurately for the Welland Canal.

• Revisions will vary.

Prepare a Presentation

Preparing for ways of thinking.

As students give feedback and revise their diagrams, look for students who:

• Excel at providing specific, useful feedback in their critiques. (Ask students to replay this discussion for the class later.)
• Attend to precision while revising their diagrams.
• Students who get stuck trying to revise their diagrams according to the feedback they received.

Challenge Problem

Make Connections

Have students share their work on their revisions.

Ask guiding questions, for example:

• How did the critique help you refine your diagram?
• What was helpful about analyzing the diagrams of your classmates?
• How did your diagram compare with the diagram of the Welland Canal shown in task 3?
• How did you label your horizontal and vertical axes? Why was this important?

As a class, critique the diagram of the Welland Canal shown in task 3. What are the strengths and weaknesses of this diagram? Ask students to compare and contrast their diagram with the one provided.

Allow students who gave focused feedback the opportunity to “replay” their critique to the class. Have students share their revisions and provide a critique as an entire class.

ELL: As ELLs explain their reasons verbally and in writing, their answers may have language errors. Remember, language mistakes are natural.Focus on the content being communicated

• Allow processing time
• Do not emphasize grammar
• Model standard English

Performance Task

Ways of thinking: make connections.

• Take notes about other classmates’ approaches to revising their diagrams.

As your classmates present, ask questions such as:

• What was the most helpful advice your partner gave you when critiquing your diagram? How did you use this advice to help you improve your diagram?
• What elements were lacking in your original diagram? How did you incorporate these elements into your new diagram?
• What is a strength of your diagram?
• How might you still improve your diagram?
• What advice would you give to help others improve their diagrams?

Reflect on Your Work

Have each student write a brief reflection before the end of class. Review the reflections to find out what students learned from looking at other students' diagrams and what revisions they made to their own diagrams.

Write a reflection about the ideas discussed in class today. Use the sentence starters below if you find them to be helpful.

From looking at other diagrams, I learned…

A revision I made to my diagram is…

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7th Grade Math Practice, Topics, Test, Problems, and Worksheets

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In 7th Grade Math Practice, you will find all Kinds of Topics explained in a clear-cut way. Keeping in mind the Child’s Level of Understanding in Grade 7 we have outlined all the concepts in a simple language so that they understand them easily. Improve your knowledge by practicing the 7th Grade Topics regularly and understand the application of concepts.

Relations and Mapping

Relations and mapping – worksheets, numbers – worksheets, fractions – worksheets, bodmas/pemdas rule, profit, loss, and discount, profit, loss and discount – worksheets, ratios and proportions, ratios and proportions – worksheets, time and work, time and work – worksheets, unitary method, unitary method – worksheets, simple interest, simple interest – worksheets, algebraic expressions, algebraic expressions – worksheets, formula – worksheets, algebraic identities, equations – worksheets, inequations, inequations – worksheets, lines and angles, polygons – worksheets.

• Quadrilateral

Symmetrical Figure

Coordinate system, mensuration, mensuration – worksheets, volume and surface area of solids.

We have compiled Practice Tests, Worksheets for the 7th Standard Math Concepts so that you can test your preparation levels. Identify the areas you are not comfortable with and allot time to them so that you can attempt them with confidence in the actual exam. After practicing from these 7th Grade Math Problems you will interpret and compute different types of topics and their problems easily.

Go Math Grade 7 Answer Key Free PDF Download

Students who wish to prepare the 7th Grade Math Concepts can check out the Chapterwise Go Math Grade 7 Answer Key available below. You just need to click on the quick links to access the concerned chapter of Go Math 7th Grade Solution Key. Clarify all your concerns easily by practicing the Step by Step Go Math Grade 7 Solutions on a daily basis.

HMH Go Math 7th Grade Answer Key

• Chapter 1: Adding and Subtracting Integers
• Chapter 2: Multiplying and Dividing Integers
• Chapter 3: Rational Numbers
• Chapter 4: Rates and Proportionality
• Chapter 5: Percent Increase and Decrease
• Chapter 6: Algebraic Expressions
• Chapter 7: Writing and Solving One-Step Inequalities
• Chapter 8: Modeling Geometric Figures
• Chapter 9: Circumference, Area, and Volume
• Chapter 10: Random Samples and Populations
• Chapter 11: Analyzing and Comparing Data
• Chapter 12: Experimental Probability
• Chapter 13: Theoretical Probability and Simulations

Big Ideas Math Book 7th Grade Answer Key

Utilize the Big Ideas Math Book Grade 7 Answer Key for all the Chapters whenever you need Homework Help. The BIM Grade 7 Answer Key available ensures you achieve your learning targets and achieve success in your exams. To make your searching experience simple we have outlined all the Big Ideas Math Grade 7 Answer Key organized as per the Big Ideas Math 7th Grade Textbooks. Simply click on the respective chapter you wanted to prepare and learn all the underlying topics in it easily.

• Chapter 1 Adding and Subtracting Rational Numbers
• Chapter 2 Multiplying and Dividing Rational Numbers
• Chapter 3 Expressions
• Chapter 4 Equations and Inequalities
• Chapter 5 Ratios and Proportions
• Chapter 6 Percents
• Chapter 7 Probability
• Chapter 8 Statistics
• Chapter 9 Geometric Shapes and Angles
• Chapter 10 Surface Area and Volume

Big Ideas Math Book 7th Grade Advanced Answer Key

Big Ideas Math Book 7th Grade Advanced Answer Key available here covers all the concepts as per the latest syllabus guidelines. Develop a Conceptual Understanding of Grade 7 Math and improve your ability to apply mathematics to solve problems. To make it easy for you we have compiled all the Chapterwise 7th Standard Math Answer Key in a simple and understandable language. You just have to click on the concerned chapter you wish to prepare and allot time accordingly.

• Chapter 1 Equations
• Chapter 2: Transformations
• Chapter 3: Angles and Triangles
• Chapter 4: Graphing and Writing Linear Equations
• Chapter 5: Systems of Linear Equations
• Chapter 6: Data Analysis and Displays
• Chapter 7: Functions
• Chapter 8 Exponents and Scientific Notation
• Chapter 9 Real Numbers and the Pythagorean Theorem
• Chapter 10 Volume and Similar Solids
• Chapter A: Equations and Inequalities
• Chapter B: Probability
• Chapter C: Statistics
• Chapter D: Geometric Shapes and Angles
• Chapter E: Surface Area and Volume

7th Grade Math Topics

On this page, you will learn all the Topics that a Grade 7 Student should learn. We have covered all the topics that a middle school student should learn as a part of the curriculum. You will find Chapters such as Integers, Fractions, Decimals, etc. Tap on the concerned chapter you wish to learn the concepts in it accordingly. You just need to tap on the direct links available and avail the topics easily.

• Objects Form a Set
• Elements of a Set
• Properties of Sets
• Representation of a Set
• Different Notations in Sets
• Standard Sets of Numbers
• Types of Sets
• Pairs of Sets
• Subsets of a Given Set
• Operations on Sets
• Union of Sets
• Intersection of Sets
• Difference of Two Sets
• Complement of a Set
• Cardinal Number of a Set
• Cardinal Properties of Sets
• Venn Diagrams
• Ordered Pair
• Cartesian Product of Two Sets
• Domain and Range of a Relation
• Functions or Mapping
• Domain Co-domain and Range of Function
• Worksheet on Math Relation
• Worksheet on Functions or Mapping
• Multiplication of Integers
• Properties of Multiplication of Integers
• Examples on Multiplication of Integers
• Division of Integers
• Absolute Value of an Integer
• Comparison of Integers
• Properties of Division of Integers
• Examples on Division of Integers
• Fundamental Operations
• Examples on Fundamental Operations
• Uses of Brackets
• Removal of Brackets
• Examples on Simplification
• Worksheet on Multiplication of Integers
• Worksheet on Division of Integers
• Worksheet on Fundamental Operations
• Worksheet on Simplification
• Types of Fractions
• Equivalent Fractions
• Like and Unlike Fractions
• Conversion of Fractions
• Fraction in Lowest Terms
• Addition and Subtraction of Fractions
• Multiplication of Fractions
• Division of Fractions
• Worksheet on Fractions
• Worksheet on Multiplication of Fractions
• Worksheet on Division of Fractions
• Decimal Numbers
• Decimal Fractions
• Decimal Places
• Decimal and Fractional Expansion
• Like and Unlike Decimals
• Conversion of Unlike Decimals to Like Decimals
• Comparing Decimals
• Adding Decimals
• Subtracting Decimals
• Simplify Decimals Involving Addition and Subtraction Decimals
• Multiplying Decimal by a Whole Number
• Multiplying Decimal by a Decimal Number
• Dividing Decimal by a Whole Number
• Dividing Decimal by a Decimal Number
• Simplification of Decimal
• Converting Decimals to Fractions
• Converting Fractions to Decimals
• Rounding Decimals
• Rounding Decimals to the Nearest Whole Number
• Rounding Decimals to the Nearest Tenths
• Rounding Decimals to the Nearest Hundredths
• Round a Decimal
• H.C.F. and L.C.M. of Decimals
• Terminating Decimal
• Non-Terminating Decimal
• Repeating or Recurring Decimal
• Pure Recurring Decimal
• Mixed Recurring Decimal
• Conversion of Pure Recurring Decimal into Vulgar Fraction
• Conversion of Mixed Recurring Decimals into Vulgar Fractions
• BODMAS Rule
• BODMAS Rules – Involving Integers
• BODMAS/PEMDAS Rules – Involving Decimals
• PEMDAS Rule
• PEMDAS Rules – Involving Integers
• PEMDAS Rules – Involving Decimals

• Concept of Profit and Loss
• Calculate Profit and Profit Percent
• Calculate Loss and Loss Percent
• Calculate Cost Price using Sell Price and Loss Percent
• Calculate Cost Price using Sell Price and Profit Percent
• Calculate Selling Price using Cost and Loss Percent
• Calculate Selling Price using Cost and Profit Percent
• Practice Test on Profit Loss and Discount
• Worksheet on Discounts
• What is a Ratio?
• What is a Proportion?
• Worksheet on Ratios
• Worksheet on Proportions
• Calculate Time to Complete a Work
• Calculate Work Done in a Given Time
• Problems on Time required to Complete a Piece a Work
• Problems on Work Done in a Given Period of Time
• Problems on Time and Work
• Pipes and Water Tank
• Problems on Pipes and Water Tank
• Worksheet on Work Done in a Given Period of Time
• Worksheet on Time Required to Complete a Piece of Work
• Worksheet on Pipes and Water Tank
• Problems Using Unitary Method
• Situations of Direct Variation
• Situations of Inverse Variation
• Direct Variations Using Unitary Method
• Direct Variations Using Method of Proportion
• Inverse Variation Using Unitary Method
• Inverse Variation Using Method of Proportion
• Problems on Unitary Method using Direct Variation
• Problems on Unitary Method Using Inverse Variation
• Mixed Problems Using Unitary Method
• Worksheet on Direct Variation using Unitary Method
• Worksheet on Direct variation using Method of Proportion
• Worksheet on Word Problems on Unitary Method
• Worksheet on Inverse Variation Using Unitary Method
• Worksheet on Inverse Variation Using Method of Proportion
• What is Simple Interest?
• Calculate Simple Interest
• Practice Test on Simple Interest
• Simple Interest Worksheet
• Division of Polynomial by Monomial
• Worksheet on Dividing Polynomial by Monomial
• Formula and Framing the Formula
• Change the Subject of a Formula
• Changing the Subject in an Equation or Formula
• Practice Test on Framing the Formula
• Worksheet on Framing the Formula
• Worksheet on Changing the Subject of a Formula
• Worksheet on Changing the Subject in an Equation or Formula
• Square of The Sum of Two Binomials
• Square of The Difference of Two Binomials
• Product of Sum and Difference of Two Binomials
• Product of Two Binomials whose First Terms are Same and Second Terms are Different
• Square of a Trinomial
• Cube of The Sum of Two Binomials
• Cube of The Difference of Two Binomials
• Cube of a Binomial
• Square of a Binomial
• What is an Equation?
• What is a Linear Equation?
• How to Solve Linear Equations?
• Solving Linear Equations
• Problems on Linear Equations in One Variable
• Word Problems on Linear Equations in One Variable
• Practice Test on Linear Equations
• Practice Test on Word Problems on Linear Equations
• Worksheet on Linear Equations
• Worksheet on Word Problems on Linear Equation
• What are Linear Inequality?
• What are Linear Inequations?
• Properties of Inequation or Inequalities
• Representation of the Solution Set of an Inequation
• Practice Test on Linear Inequation
• Worksheet on Linear Inequations

    Geometry

• Fundamental Geometrical Concepts
• Classification of Angles
• Related Angles
• Some Geometric Terms and Results
• Complementary Angles
• Supplementary Angles
• Complementary and Supplementary Angles
• Adjacent Angles
• Linear Pair of Angles
• Vertically Opposite Angles
• Parallel Lines
• Transversal Line
• Parallel and Transversal Lines
• Congruent Shapes
• Congruent Line-segments
• Congruent Angles
• Congruent Triangles
• Conditions for the Congruence of Triangles
• Side Side Side Congruence
• Side Angle Side Congruence
• Angle Side Angle Congruence
• Angle Angle Side Congruence
• Right Angle Hypotenuse Side congruence
• Pythagorean Theorem
• Proof of Pythagorean Theorem
• Converse of Pythagorean Theorem
• Word problems on Pythagorean Theorem
• Polygon and its Classification
• Terms Related to Polygons
• Interior and Exterior of the Polygon
• Convex and Concave Polygons
• Regular and Irregular Polygon
• Number of Triangles Contained in a Polygon
• Angle Sum Property of a Polygon
• Problems on Angle Sum Property of a Polygon
• Sum of the Interior Angles of a Polygon
• Sum of the Exterior Angles of a Polygon
• Worksheet on Polygon and its Classification
• Worksheet on Interior Angles of a Polygon
• Worksheet on Exterior Angles of a Polygon
• Perimeter of Quadrilateral
• Angle Sum Property of a Quadrilateral
• Missing Angle of a Quadrilateral
• Angles of a Quadrilateral are in Ratio
• Linear Symmetry
• Lines of Symmetry
• Point Symmetry
• Reflection Symmetry
• Nets of a Solids
• Rotational Symmetry
• Order of Rotational Symmetry
• Types of Symmetry
• Reflection of a Point in x-axis
• Reflection of a Point in y-axis
• Reflection of a point in origin
• 90 Degree Clockwise Rotation
• 90 Degree Anticlockwise Rotation
• 180 Degree Rotation
• Coordinate Graph
• Ordered Pair of a Coordinate System
• Plot Ordered Pairs
• Coordinates of a Point
• All Four Quadrants
• Signs of Coordinates
• Find the Coordinates of a Point
• Coordinates of a Point in a Plane
• Plot Points on Coordinate Graph
• Graph of Linear Equation
• Simultaneous Equations Graphically
• Graphs of Simple Function
• Graph of Perimeter vs. Length of the Side of a Square
• Graph of Area vs. Side of a Square
• Graph of Simple Interest vs. Number of Years
• Graph of Distance vs. Time
• Area and Perimeter
• Perimeter and Area of Rectangle
• Perimeter and Area of Square
• Area of the Path
• Area and Perimeter of the Triangle
• Area and Perimeter of the Parallelogram
• Area and Perimeter of Rhombus
• Area of Trapezium
• Circumference and Area of Circle
• Units of Area Conversion
• Practice Test on Area and Perimeter of Rectangle
• Practice Test on Area and Perimeter of Square
• Worksheet on Area and Perimeter of Rectangles
• Worksheet on Area and Perimeter of Squares
• Worksheet on Area of the Path
• Worksheet on Circumference and Area of Circle
• Worksheet on Area and Perimeter of Triangle
• Volume of Cubes and Cuboids
• Worked-out Problems on Volume of a Cuboid
• Real Life Statistics
• Terms Related to Statistics
• Frequency Distribution of Ungrouped and Grouped Data
• Use of Tally Marks
• Class Limits in Exclusive and Inclusive Form
• Construction of Bar Graphs
• Mean of the Tabulated Data
• Construction of Pie Chart
• How to Construct a Line Graph?

Grade 7 Math Goals and Objectives

Comprehensive 7th Grade Math Curriculum will concentrate on the below areas and ensure students are achieving these learning targets. They are as under

• Understand Rational Number Operations
• Representation of Rational Numbers with Decimals
• Analyze Proportional Relationships to solve mathematical problems in the real world.
• Construct and describe geometrical figures and the relationships between them.
• Solve Problems involving Angle Measure, Area, and Volume.
• Extend the use of 4 basic arithmetic operations on whole numbers, mixed numbers, decimals, and fractions.
• Analyze and Interpret Data presented in various forms.
• Solve Mathematical Problems involving numerical and algebraic expressions, equations and inequalities, etc.

Why Choose our 7th Grade Math Curriculum?

Master the concepts of Grade 7 Math and study advanced mathematics in a fun learning way. They are as follows

• 7th Grade Math Practice helps you to achieve learning targets and master the concepts easily.
• Our Preparation Material keeps students engaged irrespective of their learning method.
• You can access the 7th Grade Math Topics 24/7 from anywhere for free of cost.
• 7th Grade Math Worksheets and Practice Tests available make it easy for you to learn challenging concepts too even after school.
• Learning Exercises and Simulated Assessments provide 7th Grade Standardized Test Practice.

We wish the knowledge shed regarding the 7th Grade Math Topics has enlightened you. If you have any suggestions do leave us your feedback so that we can look into them and add if necessary. Keep in touch with our site to avail latest updates on Gradewise Math Topics in no time.

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The Algebra Problem: How Middle School Math Became a National Flashpoint

From suburbs in the Northeast to major cities on the West Coast, a surprising subject is prompting ballot measures, lawsuits and bitter fights among parents: algebra.

Students have been required for decades to learn to solve for the variable x, and to find the slope of a line. Most complete the course in their first year of high school. But top-achievers are sometimes allowed to enroll earlier, typically in eighth grade.

The dual pathways inspire some of the most fiery debates over equity and academic opportunity in American education.

Sign up for The Morning newsletter from the New York Times

Do bias and inequality keep Black and Latino children off the fast track? Should middle schools eliminate algebra to level the playing field? What if standout pupils lose the chance to challenge themselves?

The questions are so fraught because algebra functions as a crucial crossroads in the education system.

Students who fail it are far less likely to graduate. Those who take it early can take calculus by 12th grade, giving them a potential edge when applying to elite universities and lifting them toward society’s most high-status and lucrative professions.

But racial and economic gaps in math achievement are wide in the United States, and grew wider during the pandemic. In some states, nearly 4 in 5 poor children do not meet math standards.

To close those gaps, New York City’s previous mayor, Bill de Blasio, adopted a goal embraced by many districts elsewhere. Every middle school would offer algebra, and principals could opt to enroll all of their eighth graders in the class.

San Francisco took an opposite approach: If some children could not reach algebra by middle school, no one would be allowed to take it.

The central mission in both cities was to help disadvantaged students. But solving the algebra dilemma can be more complex than solving the quadratic formula.

New York’s dream of “algebra for all” was never fully realized, and Mayor Eric Adams’ administration changed the goal to improving outcomes for ninth graders taking algebra. In San Francisco, dismantling middle-school algebra did little to end racial inequities among students in advanced math classes. After a huge public outcry, the district decided to reverse course.

“You wouldn’t think that there could be a more boring topic in the world,” said Thurston Domina, a professor at the University of North Carolina. “And yet, it’s this place of incredibly high passions.”

“Things run hot,” he said.

In some cities, disputes over algebra have been so intense that parents have sued school districts, protested outside mayors’ offices and campaigned for the ouster of school board members.

Teaching math in middle school is a challenge for educators in part because that is when the material becomes more complex, with students moving from multiplication tables to equations and abstract concepts. Students who have not mastered the basic skills can quickly become lost, and it can be difficult for them to catch up.

Many school districts have traditionally responded to divergent achievement levels by simply separating children into distinct pathways, placing some in general math classes while offering others algebra as an accelerated option. Such sorting, known as tracking, appeals to parents who want their children to reach advanced math as quickly as possible.

But tracking has cast an uncomfortable spotlight on inequality. Around a quarter of all students in the United States take algebra in middle school. But only about 12% of Black and Latino eighth graders do, compared with roughly 24% of white pupils, a federal report found.

“That’s why middle school math is this flashpoint,” said Joshua Goodman, an associate professor of education and economics at Boston University. “It’s the first moment where you potentially make it very obvious and explicit that there are knowledge gaps opening up.”

In the decades-long war over math, San Francisco has emerged as a prominent battleground.

California once required that all eighth graders take algebra. But lower-performing middle school students often struggle when forced to enroll in the class, research shows. San Francisco later stopped offering the class in eighth grade. But the ban did little to close achievement gaps in more advanced math classes, recent research has found.

As the pendulum swung, the only constant was anger. Leading Bay Area academics disparaged one another’s research. A group of parents even sued the district last spring. “Denying students the opportunity to skip ahead in math when their intellectual ability clearly allows for it greatly harms their potential for future achievement,” their lawsuit said.

The city is now back to where it began: Middle school algebra — for some, not necessarily for all — will return in August. The experience underscored how every approach carries risks.

“Schools really don’t know what to do,” said Jon R. Star, an educational psychologist at Harvard who has studied algebra education. “And it’s just leading to a lot of tension.”

In Cambridge, Massachusetts, the school district phased out middle school algebra before the pandemic. But some argued that the move had backfired: Families who could afford to simply paid for their children to take accelerated math outside school.

“It’s the worst of all possible worlds for equity,” Jacob Barandes, a Cambridge parent, said at a school board meeting.

Elsewhere, many students lack options to take the class early: One of Philadelphia’s most prestigious high schools requires students to pass algebra before enrolling, preventing many low-income children from applying because they attend middle schools that do not offer the class.

In New York, de Blasio sought to tackle the disparities when he announced a plan in 2015 to offer algebra — but not require it — in all of the city’s middle schools. More than 15,000 eighth graders did not have the class at their schools at the time.

Since then, the number of middle schools that offer algebra has risen to about 80% from 60%. But white and Asian American students still pass state algebra tests at higher rates than their peers.

The city’s schools chancellor, David Banks, also shifted the system’s algebra focus to high schools, requiring the same ninth-grade curriculum at many schools in a move that has won support and backlash from educators.

And some New York City families are still worried about middle school. A group of parent leaders in Manhattan recently asked the district to create more accelerated math options before high school, saying that many young students must seek out higher-level instruction outside the public school system.

In a vast district like New York — where some schools are filled with children from well-off families and others mainly educate homeless children — the challenge in math education can be that “incredible diversity,” said Pedro A. Noguera, the dean of the University of Southern California’s Rossier School of Education.

“You have some kids who are ready for algebra in fourth grade, and they should not be denied it,” Noguera said. “Others are still struggling with arithmetic in high school, and they need support.”

Many schools are unequipped to teach children with disparate math skills in a single classroom. Some educators lack the training they need to help students who have fallen behind, while also challenging those working at grade level or beyond.

Some schools have tried to find ways to tackle the issue on their own. KIPP charter schools in New York have added an additional half-hour of math time to many students’ schedules, to give children more time for practice and support so they can be ready for algebra by eighth grade.

At Middle School 50 in Brooklyn, where all eighth graders take algebra, teachers rewrote lesson plans for sixth- and seventh-grade students to lay the groundwork for the class.

The school’s principal, Ben Honoroff, said he expected that some students would have to retake the class in high school. But after starting a small algebra pilot program a few years ago, he came to believe that exposing children early could benefit everyone — as long as students came into it well prepared.

Looking around at the students who were not enrolling in the class, Honoroff said, “we asked, ‘Are there other kids that would excel in this?’”

“The answer was 100%, yes,” he added. “That was not something that I could live with.”

c.2024 The New York Times Company

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The Government Takes On Ticketmaster

Explaining a case that could reshape the multibillion-dollar live entertainment industry..

Hosted by Sabrina Tavernise

Featuring David McCabe

Produced by Will Reid ,  Rob Szypko and Rachelle Bonja

Edited by Brendan Klinkenberg and Michael Benoist

Original music by Marion Lozano ,  Dan Powell and Will Reid

Engineered by Alyssa Moxley

Listen and follow The Daily Apple Podcasts | Spotify | Amazon Music | YouTube

Over recent years, few companies have provoked more anger among music fans than Ticketmaster. Last week, the Department of Justice announced it was taking the business to court.

David McCabe, who covers technology policy for The Times, explains how the case could reshape America’s multibillion-dollar live music industry.

On today’s episode

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Background reading

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We aim to make transcripts available the next workday after an episode’s publication. You can find them at the top of the page.

The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Mike Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, John Ketchum, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Summer Thomad, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Renan Borelli, Maddy Masiello, Isabella Anderson, Nina Lassam and Nick Pitman.

David McCabe covers tech policy. He joined The Times from Axios in 2019. More about David McCabe

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