problem solving question year 2

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Year 2 Maths Worksheets UK Hub Page

Welcome to Math Salamanders Year 2 Maths Worksheets hub page.

In our Year 2 area, you will find a wide range of printable math worksheets and Maths activities for your child to enjoy.

Come and take a look at our dot-to-dot pages, or our maths games. Perhaps you would prefer our 2d shape worksheets, or learning about numbers using our number line worksheets?

Hopefully you will find something here to meet your child's maths requirements!

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• This page contains links to other Math webpages where you will find a range of activities and resources.
• If you can't find what you are looking for, try searching the site using the Google search box at the top of each page.

Year 2 Maths Learning

Here are some of the key learning objectives for the end of Year 2:

• know and use Place value up to 100
• Compare and order numbers up to 100
• Counting on and back in 1s and 10s
• count in 2s, 5s and 10s
• Position numbers on a number line up to 1000
• use addition and subtraction facts to 20
• use related facts for addition and subtraction
• add or subtract 1 or 10 from a 2-digit number
• add and subtract 2-digit numbers
• number bonds to 100 using tens only
• add three single-digit numbers
• recognise and make equal groups
• use the x symbol to write multiplication sentences
• use arrays and pictures to represent multiplication sentences
• know multiplication facts for the 2, 5 and 10 times table
• recognise and find a half, a quarter and a third
• understand and use fraction notation
• understand the equivalence of a half and two-quarters
• count on in halves, thirds and quarters up to 10
• count in pence: 1p, 2p ,5p, 10p and 20p
• count in pounds: £1, £2, £5, £10 and £20
• find a simple total or difference between two money amounts
• find the change from simple amounts
• tell the time: o'clock, half-past, quarter-past and to
• understand and compare durations of time
• compare and measure length, mass, volume, capacity and temperature
• read a variety of scales going up in 1s, 2s, 5s and 10s
• recognise 2D and 3D shapes
• count sides and vertices on 2D shapes
• count faces, edges and vertices on 3D shapes
• sort and make patterns with 2D and 3D shapes
• describe movement and turns
• make tally charts
• draw and interpret pictograms
• understand and use block diagrams

Please note:

Our site is mainly based around the US Elementary school math standards.

Though the links on this page are all designed primarily for students in the US, but they are also at the correct level and standard for UK students.

The main issue is that some of the spelling is different and this site uses US spelling.

Year 2 is generally equivalent to 1st Grade in the US.

On this page you will find link to our range of math worksheets for Year 2.

Quicklinks to Year 2 ...

• Place Value Zone

Operations Zone

• Mental Math Zone

Word Problems Zone

• Measurement Zone

Geometry Zone

Data analysis zone.

• Fun Zone: games and puzzles

Coronavirus Stay At Home Support

For those parents who have found themselves unexpectedly at home with the kids and need some emergency activities for them to do, we have started to develop some Maths Grab Packs for kids in the UK.

Each pack consists of at least 10 mixed math worksheets on a variety of topics to help you keep you child occupied and learning.

The idea behind them is that they can be used out-of-the-box for some quick maths activities for your child.

They are completely FREE - take a look!

• Free Maths Grabs Packs

Place Value & Number Sense Zone

Year 2 Place Value Charts

Here you will find a range of Free Printable Place Value Charts for Year 2.

These printable charts will help your child learn to read and write numbers.

Some of the charts are partially filled to help your child learn their place value.

Using these sheets will help your child to:

• learn to count in tens and ones;
• learn to read and write numbers.
• Printable Number Charts 0-99
• Hundred Number Charts (100 Squares)
• Number Grid up to 200

Place Value and Counting Worksheets

Here you will find a range of Year 2 Place Value Worksheets.

These Year 2 maths worksheets will help your child learn their place value, reading, writing and ordering numbers up to 100.

There are also some money worksheets involving counting in dimes and pennies to support place value learning.

• learn to order numbers to 100;
• learn to count in dimes and pennies;
• learn to read and write numbers to 100.

Year 2 Place Value Worksheets

• Place Value to 20 Worksheets
• Math Place Value Worksheets Tens and Ones
• Ordering 2-digit numbers Worksheets
• Greater than Less than Worksheets - up to 2 digit numbers
• Printable Counting Worksheets to 50
• Missing Number Chart 1-100
• Counting by 2s Worksheets
• Math Worksheets Counting by 1s 5s and 10s

Number Line Worksheets

Here is our selection of free printable number line worksheets for Year 2 pupils.

These first grade math worksheets will give your child a good grasp of place value and number sequences up to 100.

• count on and back by ones;
• position numbers to 100 on a number line.
• Number lines to 20
• Number lines to 100

Year 2 Mental Maths Zone

Here you will find a range of printable mental math sheets designed especially for Year 2 children.

Each quiz tests the children on a range of math topics from number facts and mental arithmetic to geometry, solving word problems and measures questions.

A great way to revise topics, or use as a weekly math quiz!

• Year 2 Printable Mental Maths

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Year 2 Addition Worksheets

Here you will find a range of Free Printable Addition Worksheets to support Year 2.

The following first grade math worksheets involve adding different amounts.

• learn their addition facts to 12+12;
• learn to solve an addition fact where one of the addends is missing;
• learn to add numbers in columns up to 100.
• Number Bonds to 10 and 12
• Addition Sentences to 12
• Addition Fact Practice to 12
• Addition Facts to 20 Worksheets
• Adding tens
• Addition Word Problems
• 2 Digit Addition Without Regrouping
• 2 Digit Addition Worksheets With Regrouping
• Free Addition Worksheets (randomly generated)

Year 2 Subtraction Worksheets

Here you will find a range of Year 2 Subtraction Worksheets.

The following worksheets involve using the Math skills of subtracting.

Using these Year 2 maths worksheets will help your child to:

• learn their addition and subtraction facts to 12;
• learn to subtract 2 digit numbers.
• Subtraction Facts to 12
• Subtracting tens
• Subtraction Word Problems
• Two Digit Subtraction Worksheets Without Regrouping
• 2 Digit Subtraction Worksheets With Regrouping
• Free Subtraction Worksheets (randomly generated)

Addition & Subtraction Worksheets

If you need to mix and match addition and subtraction fact questions within the same sheet, then use this section here.

The addition and subtraction worksheets involve counting on and back with numbers to 12.

• Math Activities Addition and Subtraction to 12
• Add and Subtract 10 Worksheets
• Addition Subtraction Worksheets (randomly generated)
• Addition and Subtraction Problems

Year 2 Maths Word Problems

Here you will find a range of math word problems aimed at Year 2 level. Each problem sheet is based on an interesting theme such as parties or the seaside.

• Add and subtract with numbers to 12;
• order numbers to 100;
• solve a range of math problems.
• Maths Problems for Year 2

Longer Math Problems

• Year 2 Maths Problems (1st Grade)

Year 2 Geometry Worksheets

Here is a range of free geometry worksheets for Year 2 pupils.

The following worksheets will help your child to:

• Identify and name a range of 2d and 3d shapes;
• Draw 2d shapes;
• Know some of the properties of 2d shapes.
• Year 2 Geometry Worksheets (1st Grade)

Measurement Zone, including Time & Money

Year 2 measurement worksheets.

Here is our selection of measurement worksheets for Year 2 pupils.

These sheets involve reading scales going up in ones to find the weight or liquid capacity.

Using these sheets will help children to consolidate their counting as well as learning to read a simple scale.

• Year 2 Measurement Worksheets (1st Grade)

Year 2 Money Worksheets

Here you will find a range of free printable First Grade Money Worksheets.

The following worksheets involve counting different amounts of money in pennies, nickels and dimes.

• learn the names and values of the US coins;
• learn to count up different amounts of money to £1 in coins.
• Free Counting Money Worksheets UK Coins (easier)
• Free Money Worksheets UK Coins up to £1

Printable Money Resources

• Printable Money Flashcards
• Kids Counting Money Dominoes

Telling the Time Worksheets

Here is our selection of telling the time worksheets for 1st grade.

• read o'clock and half-past times;
• convert o'clock and half-past times to digital;
• draw clock hands correctly to mark out o'clock and half-past.

The year 2 maths worksheets in this section will help your child learn to tell simple times on an analogue clock.

• Telling Time Worksheets o'clock and half-past
• Clock Worksheets - Quarter Past and Quarter To

Year 2 Bar Graph Worksheets

Here is our selection of bar graphs for first graders.

These Year 2 maths worksheets involve reading and interpreting a range of bar graphs and picture graphs with a scale going up in ones.

Using these sheets will help children to understand how bar graphs work.

• Year 2 Picture/Bar Graphs (First Grade)

Fun Zone: Puzzles, Games and Riddles

Year 2 Maths Games

Here you will find a range of free printable Math games. All children like to play Math games, and you will find a good range of Maths Games at a Year 2 level here for your child to play and enjoy.

• Year 2 Maths Games (First Grade)

Year 2 Maths Puzzles

Here you will find a range of printable Year 2 level math puzzles for your child to enjoy.

The puzzles will help your child practice and apply their addition and subtraction facts as well as developing their thinking and reasoning skills in a fun and engaging way.

Using these puzzles will help your child to:

• develop thinking and reasoning skills;
• develop perseverance.
• Year 2 Maths Puzzles (1st Grade)
• Dot to Dot up to 50

Math Salamanders Year 2 Maths Games Ebook

Our Year 2 Maths Games Ebook contains all of our fun maths games, complete with instructions and resources.

This ebooklet is available in our store - use the link below to find out more!

• Year 2 Maths Games Ebook

Other UK Maths Worksheet pages

See below for our other maths worksheets hub pages designed for children in the UK.

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The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.

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45 year 2 maths questions

Learn how to master year 2 maths word problems with these 45 maths questions! Answers included.

Author Michelle Griczika

Published February 2024

• Key takeaways
• Addition & Subtraction : Adding and subtracting numbers is like solving puzzles and helps us with real-life situations.
• Word Problems : Solving word problems makes maths fun and helps us become better readers and problem solvers.
• Place Value : Understanding place value helps us read and write numbers correctly and compare their values.
• Measurement & Time : Measuring objects and telling time help us understand the world around us and manage our daily routines.
• Geometry (Shapes) : Recognizing shapes and their properties helps us see the world in a new way and understand how things are put together.

Table of contents

• Addition and Subtraction
• Word Problems
• Place Value
• Geometry (Shapes)

Did you know that ladybugs have spots on their backs?

If a ladybug has 2 spots on its back and it gets 1 more spot, how many spots will the ladybug have in total?

The lady bug will have 3 spots!

Year 2 maths word problems are like fun puzzles that help us use our maths skills to solve real-life situations. They are essential to year 2 maths, and practising them can help us become maths superstars!

• We can use addition and subtraction to determine how many cookies are left in a jar, how many friends are on the playground, or even how many apples are in a basket.
• Understanding place value is like being a number detective. It helps us read big numbers and know the value of each digit, so we can count things like how many toys we have or how many days until our birthday.
• Measuring things and telling time is like being an explorer in the real world. We can measure how tall we are, how long a pencil is, or even how much water is in a glass. And knowing how to read a clock helps us know when it’s time for fun activities or when it’s time to go to bed.
• Shapes are like building blocks of the world around us. We can learn about squares, triangles, and circles by looking at objects we see every day. It’s like being a shape detective, finding out how many sides and corners they have, and how they fit together like puzzle pieces in year 2 maths questions.

All of these skills are necessary for year 2 maths practice! Use these 45 maths questions to go over important maths skills needed to strengthen your student’s understanding and knowledge.

Today, we are going to practise different year 2 maths skills that cover measurement, addition and subtraction, and more! Once you are done, check your work with our answer sheet!

Section 1: Addition & subtraction

Section 2: word problems, section 3: place value, section 4: geometry (shapes), section 5: time.

What time is the clock below telling?

Time answer sheet

Parents, sign up for a DoodleMaths subscription and see your child become a maths wizard!

Lesson credits

Michelle Griczika

Michelle Griczika is a seasoned educator and experienced freelance writer. Her years teaching first and fifth grades coupled with her double certification in elementary and early childhood education lend depth to her understanding of diverse learning stages. Michelle enjoys running in her free time and undertaking home projects.

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Free Year 2 Maths Worksheets And Homework: Printable, Downloadable Or Just View Online

Sophie Bessemer

Here you can find all our free Year 2 maths worksheets and Year 2 maths resources, many of which are suitable for homework and home learning .

All our KS1 and KS2 maths worksheets are printable and most are in pdf format, but they can also be viewed online too. If you’re looking for other slides-based teaching resources and lesson plans, we recommend you look at our range of White Rose maths lessons.

The hope is that these pdf Year 2 maths worksheets and free resources can be used with minimal support from parents as part of a 6 or 7 year old’s Year 2 maths homework routine and by teachers as part of a planned lesson framework.

For parents working with their children at home we would recommend you focus on practising and improving pupils’ core numeracy skills using the numbers worksheets as these generally require less input than topics like geometry – 2d shapes and 3d shapes. Place value and number after all are the building blocks of Key Stage 1 and later Key Stage 2 maths.

We have also included some telling the time worksheets; these will require support from a teacher or parent but the method used is truly revolutionary.

National curriculum guidance is given where relevant and each Year 2 worksheet includes answer sheets.

If you’re a parent then our home learning hub is full of home learning packs , workbooks, tips and further teaching ideas for Year 2 Maths at home and maths homework . 

If you’re a teacher or school leader who is interested in improving maths attainment in your school or classroom, then Third Space Learning is here to support you with our online tutoring programme of maths interventions , together with maths resources and CPD.

Free Year 2 Maths Worksheets and Tests

Register now with the Third Space Maths Hub (Use Chrome) to download all our free Year 2 maths worksheets, workbooks and resources

Year 2 Free Place Value Worksheets

Year 2 free addition, subtraction, multiplication, division worksheets, year 2 free fractions worksheets , other year 2 free worksheets .

• Also in this series…

Year 2 Maths Worksheets on place value: Worked Examples

Understanding place value is essential for all children of any age. In Year 2, children will need to know the value of digits in a two digit number as well as comparing numbers and continuing sequences. This worksheet shows children common errors that are made in the place value topic. Children then become ‘the teacher’ and check the answers and explain any errors they find. 

Download Year 2 place value worksheets: Worked Examples

Year 2 Maths Worksheets on addition and subtraction: Worked Examples

In Year 2, children will focus on adding and subtracting 2-digit numbers. It is important that children know addition and subtraction facts they were taught in Year 1, for example number bonds . This worksheet focuses on a range of addition and subtraction problems that have been incorrectly solved. Children will need to check and correct questions such as subtracting using a bar model, using known facts and missing number problems. 

Download Year 2 addition and subtraction worksheets: Worked Examples

Year 2 Maths Worksheets on multiplication and division: Independent Recap

Children will start to focus on more formal methods of multiplication and division when in Year 2, including understanding patterns in the 2s, 5s and 10s times tables . These worksheets allow children to work independently on the ten times tables, odd and even numbers, grouping and sharing through a range of question types (word problems, fluency questions and so on). 

Download Year 2 multiplication and division worksheets: Independent Recap

Year 2 Maths Worksheets on multiplication and division: Worked Examples

There are many misconceptions that can form when first looking at multiplication and division. This worksheet focuses on addressing common misconceptions or errors in multiplication and division. The worksheet covers understanding what equal groups are, the relationship between repeated addition and multiplication as well as finding missing numbers in given calculations. 

Download Year 2 multiplication and division worksheets: Worked Examples

Year 2 Maths Worksheets on times tables: Ultimate Times Tables 

In Year 2, children will start to learn their times tables after learning to count in 2s, 5s and 10s in Year 1. These games are a fun way of learning times table facts, including the related inverse division calculations.  

Download Year 2 times tables worksheets: Ultimate Times Tables

Year 2 Maths Worksheets on fractions: Independent Recap

There is a lot of new vocabulary introduced in fractions in Year 2 (including the use of actual fractions). These worksheets allow children to work independently through the new vocabulary and concepts introduced, so would be useful for homework or home learning tasks. The worksheets work through unit fractions and non-unit fractions, finding a half and finding a quarter. For each worksheet, there is at least one question that encourages children to explain their answers and develop their reasoning skills. 

Download Year 2 fractions worksheets: Independent Recap

Year 2 Maths Worksheets on fractions: Worked Examples

Many children struggle with the concept of fractions. At a young age, children can develop a range of misconceptions that could under them in future years. This worksheet aims to identify common misconceptions and errors children make in the Year 2 fractions topic (such as a fraction being equal parts) and encourage them to discuss them. 

Download Year 2 fractions worksheets: Worked Examples

Year 2 Maths Worksheets for improving mental maths skills, arithmetic and fluency: Fluent in Five

We recommend every primary school child starts their day with Fluent in Five. It’s 5-10 minutes of daily arithmetic questions and is available for every primary school year group. In Year 2 children have 3 questions per day to answer. They are given prompts of concrete or pictorial resources (such as counters or number lines) they could use to help them solve the question presented to them. You’d be amazed at how quickly young people will build their number confidence with this resource. 

Download Year 2 arithmetic worksheets: Fluent in Five

Year 2 Maths worksheets for telling the time

For some reason learning to tell the time proves a challenge for most children, regardless of their prior attainment in maths. If you have a child who’s struggling with telling the time these worksheets provide a step by step process to help them master it. The key is to start with a number line.

Download KS1 telling the time: Activity Worksheets

Year 2 maths games worksheets and activities

Getting children fully engaged can be a struggle at times, especially towards the end of the summer term. We have over 20 great ideas for KS1 maths games which bring out the fun side of problem solving and get children excited about maths. Each gameplay outline includes a ‘What You Will Need’ section, so that you can be fully prepared to bring out Fraction Snap or Subtraction Bowling during your next lesson.  

Download Year 2 maths games and activities resource pack

Read More: 25 Fun Maths Games For Kids To Do At Home For Free!

Also in this series…

• Year 3 Maths Curriculum Toolkit for 6 & 7 Year Olds
• Year 3 Maths Worksheets
• Year 4 Maths Curriculum Toolkit for 7 & 8 Year Olds
• Year 4 Maths Worksheets
• Year 5 Maths Curriculum Toolkit for 9 & 10 Year Olds
• Year 5 Maths Worksheets
• Year 6 Maths Curriculum Toolkit for 10 & 11 Year Olds
• Year 6 Maths Worksheets

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Learn how tutors develop pupils’ maths fluency or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

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Free Year 5 Maths Worksheets And Homework – Download, Print, Or View Online

FREE Fluent in Five Weeks 1 to 6 (Years 1 to 6)

Easy to implement daily arithmetic questions to build number fluency and confidence in 5 minutes a day.

Downloaded by 38,840+ teachers.

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Reasoning/Problem Solving

Year 2 Reasoning

Many schools are using some of the ideas of the ‘mastery programme’ as used in Singapore and other parts of the Far East. The aim of this programme is to give children a deep understanding and fluency in the fundamentals of maths. Because this understanding is deep it will not have to be re-taught at a later time; something which happens all too often at the moment.

This new approach needs new resources, especially geared towards reasoning and problem solving. Thankfully we have always considered reasoning to be a key part of the maths curriculum and many of our resources in all categories are designed for this. But we also have a separate category in each year group called, ‘Reasoning and Problem Solving’ where you will find a rich source of material.  In Year 2 we have a large selection of  ‘How many ways ….’ type of practical exercises (e.g. How many different ways can you score 12 with 3 dice?) These encourage children to think logically and order their results so that they can be sure that they have all possible answers. A favourite of mine is the ‘Two Coin Challenge’. Progressing from these practical tasks are the more abstract challenges such as making 2-digit numbers from a set of number cards.

Finally, take some time out to play the maths games such as Nim which originated in China. They are great at developing logical thinking and developing a winning strategy. You should never lose if you go first! These pages really are not to be missed and we thoroughly recommend them.  

Money and shopping

Solving problems involving money and shopping.

What coins could you receive when given 10p change?

What totals can be made from just two coins?

I've got three coins. They are all different. What possible totals could I have?

Can I use just 7 coins to pay all amounts up to 20p?

Solving problems about shopping: quite tricky.

More solving problems about shopping: quite tricky.

Buy shapes which are priced according to the number of sides.

'How many ways' investigations

Challenges which ask how many possible ways there are to solve a problem.

Three boxes and 20 buttons. How many different ways can the buttons be put in the boxes so that each box has an even number?

19 buttons to sort into odd numbers.

How many presents could each of the three girls have got from a total of 20. They all got an even number of presents!

How many ways can the apples be put in the boxes so that there is an even number of apples in each box?

How many ways can the balloons be coloured? A logical thinking exercise.

How many different addition, subtraction and multiplication questions can be made with the cards shown?

How many different addition sentences can be made using the numbers shown?

Create a number plate for the gorillas new car: but you can only use the digits 1, 2 or 3!

How many different ways can various jars be filled with jam?

How many different ways can various buckets be filled with water?

How many different ways can various containers be filled with shampoo?

How many different ways can various containers be filled with bubble bath?

Investigating combinations of fruit.

Investigating combinations of packs of toy farm animals.

Investigating combinations of groups of children.

Find all the ways of jumping forward.

Three very athletic runners sharing a 19 mile relay. They each run an odd number of miles. How could they do this?

Mini investigations into how many different ways totals can be made from three numbers.

A mini investigation for superbrains. How many ways can you make 100, just using the numbers and signs shown?

Can you find 10 different ways of making 12 with 3 cards? (One card is zero, which makes it trickier!)

Number challenges

A variety of number problems and challenges

Making 2-digit numbers.

Using only the numbers 3 and 2 and the + and - signs, can all the numbers up to 20 be made?

A colourful set of number problems involving beads.

Colourful pages on solving number problems involving buttons.

Roll two dice and add the totals. Record and sort the results. What do you notice?

How many different ways can you score a total with two dice?

Using grids to reason about place value of numbers.

Use three dice to see how many different ways a score of 12 can be made.

Solve number problems with dice (1)

More number problems with dice.

Find as many ways as possible to complete the number sentence.

Make and order 2-digit numbers from a selection of number cards.

Number sentences with missing digits using addition, subtraction, multiplication and division.

Recognising that subtraction is the inverse of addition and the relationship between multiplication and division.

All the signs are missing. Find the correct signs to complete the number sentences.

Put the addition or subtraction signs in to make the number sentences correct. Hard, as there is more than one sign!

Problem solving: finding the right sign.

How many patterned tiles are there altogether?

Find how many tiles there are in the pattern.

Further challenges and investigations

More great investigations and challenges for children in Year 2.

Place the toys on the correct shelves.

Use the balance scales to work out which shelves the items go on.

These pages are all to do with sequencing.

Finding the lengths of pencils in a line.

Finding more than the given numbers.

Monsters and legs problems.

Writing addition statements as multiplication.

Put the numbers in the boxes so that the total of the row across adds up to the same as the total of the column down. Several ways to do this, leading to further investigations.

How long will it take to complete a page of addition, subtraction, multiplication and division questions?

Find a route through the maze from IN to OUT adding the numbers as you go.

Dominoes are a great resource for sorting. Try these ideas to begin with.

Roll two dice and add the totals. Record and sort results.

Sam's got a great aim but how many can he score with four beanbags?

What possible scores could I get with four darts?

Harder four dart totals.

Word problems

Use knowledge of maths to solve problems written in words.

Some tricky word problems to solve.

A great selection of one and two-step word problems.

More tricky one-step and two-step word problems.

Addition and subtraction related to the six digits shown.

A selection of mathematical games for one or more players.

An easy version of the game of Nim. Great for logical thinking and you can always win (if you know what you are doing!)

The very simplest forms of magic squares and some ideas on how to turn them into colour patterns.

How many counters can you place on the grid without getting 3 in a row?

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Reasoning and Problem Solving Questions Collection - KS1 and KS2

Subject: Mathematics

Age range: 5-7

Resource type: Worksheet/Activity

Last updated

10 March 2023

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These booklets each contain over 40 reasoning and problem solving questions suitable for KS1, KS2 and KS3 classes. These are the questions that we have been putting out each day in March 2016 on Twitter in the run up to SATS.

The answers are provided with some simple notes at the back of the booklet and for some problems supplementary questions and variation has been provided.

As always we welcome any feedback on the work we are doing and the materials that we are releasing. Thank you for taking an interest in our work. The White Rose Maths Hub Team

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We are pleased to let you know that your resource Reasoning and Problem Solving Questions Collection - KS1 and KS2, has been hand-picked by the Tes resources content team to be featured in https://www.tes.com/teaching-resources/blog/fluency-reasoning-and-problem-solving-primary-maths in April 2024 on https://www.tes.com/teaching-resources/blog. Congratulations on your resource being chosen and thank you for your ongoing contributions to the Tes Resources marketplace.

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A very good and engaging way to teach mastery of maths. Thank you for sharing

thank you for sharing, this is really good

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2nd Grade Math Word Problems Worksheets

Math word problem worksheets for grade 2.

These word problem worksheets place 2nd grade math concepts in contexts that grade 2 students can relate to.  We provide math word problems for addition, subtraction, multiplication, time, money and fractions.

We encourage students to read and think about the problems carefully, and not just recognize an answer pattern.  We facilitate this by:

• providing a number of mixed word problem worksheets (e.g. subtraction questions mixed in with addition questions)
• sometimes including irrelevant data within word problems so students must understand the context before applying a solution

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New Orleans teens solve 2,000-year-old math problem

W hen she started a math contest with a bonus question challenging students to create a new proof for the Pythagorean theorem using trigonometry, teacher Michelle Blouin Williams didn’t expect anyone to complete the task.

“I was just looking for some ingenuity,” she said, per CBS News .

Calcea Johnson and Ne’Kiya Jackson, however, blew Williams’ expectations out of the water by figuring it out in 2023. The teens were seniors at St. Mary’s Academy in New Orleans, a prestigious Catholic school for girls which has maintained a 100% acceptance rate to colleges and 100% graduation rate for 17 years, CBS News reported.

They appeared in an episode of CBS News’ “60 Minutes ” on Sunday to talk about their achievement.

How did the teens find the answer?

While they were motivated initially by the math competition’s $500 prize, an internal drive to finish what they started manifested when they reached the tricky bonus question. For two months, the high school seniors worked tirelessly to finish their proof.

CeCe Johnson, Calcea’s mother, told “60 Minutes,” “It was pages and pages and pages of, like, over 20 or 30 pages for this one problem.”

Her father, Cal Johnson, added, “Yeah, the garbage can was full of papers, which she would, you know, work out the problems and — if that didn’t work she would ball it up, throw it in the trash.”

When they finished, teachers at St. Mary’s recognized the importance of their work and submitted their proof to the American Mathematical Society for recognition at a conference in March 2023, where the students presented their work.

What is the Pythagorean theorem and what’s a proof?

In essence, the mathematical theorem states that knowing the lengths of two sides of a right triangle enables you to figure out the length of the third using this formula: a² + b² = c².

It’s associated with Greek mathematician Pythagoras, but evidence suggests it was known earlier, in Babylon and Iron Age India, per Britannica . Its practical uses include construction and architecture, two-dimensional navigation, and surveying.

A mathematical proof is exactly what it sounds like: reasoning that proves a mathematical theorem is true. American mathematician Daniel Kane explains proofs as being like essays, but using math.

Why is Calcea Johnson and Ne’Kiya Jackson’s work significant?

According to the “ 60 Minutes ” episode, “there had been more than 300 documented proofs of the Pythagorean Theorem using algebra and geometry, but for 2,000 years a proof using trigonometry was thought to be impossible.”

In 1927, mathematician Elisha Loomis said as much in his book, “ The Pythagorean Proposition .” Loomis argued that there could be no trigonometric proof of the theorem because it would be circular.

Stuart Anderson, a professor emeritus of mathematics at Texas A&M University–Commerce, told Scientific American , “A lot of the basic trig ‘identities’ are nothing more than Pythagoras’ theorem.”

So, because trigonometric functions are based upon the Pythagorean theorem, using them reflexively to prove the theorem would be akin to going in circles and a fundamental mathematical error, Loomis argued.

According to Scientific American , the teens refuted this in their presentation in 2023 and said that “a trigonometric identity called the law of sines didn’t depend on the Pythagorean theorem and that they could use it to prove the theorem.”

Calcea and Ne’Kiya have joined an extremely small group who’ve accomplished the same feat, including mathematician Jason Zimba, who successfully created a new proof in 2009. The two submitted their proof for final peer review this spring and continue to work on creating more proofs.

How did the world respond to their accomplishment?

The teens were given the keys to the city of New Orleans and a commendation from the governor of Louisiana, among other public recognitions.

While their achievement “blew up,” as Ne’Kiya described it, the two students remain humble, and laughed at being called geniuses.

When news of their accomplishment broke, some people seemed to be shocked and dismissed the news as fake, St. Mary’s president Pamela Rogers said in the interview .

“They were saying, ‘Oh, they could not have done it. African Americans don’t have the brains to do it.’ ... People — have a vision of who can be successful. And — to some people, it is not always an African American female. And to us, it’s always an African American female.”

When interviewer Bill Whitaker asked why they thought there’d been such a response, Ne’Kiya said, “Probably because we’re African American, one. And we’re also women. So I think — oh, and our age. Of course our ages probably played a big part.”

“I’d like to actually be celebrated for what it is. Like, it’s a great mathematical achievement,” she continued.

Watch CBS News

Teens surprise math world with Pythagorean Theorem trigonometry proof | 60 Minutes

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As Kentucky Derby Nears, Last Year’s Deaths Cast Long Shadow

The breakdown of 12 horses in the days surrounding the celebrated race a year ago has led to existential questions about the sport and its future.

Last year at Churchill Downs, seven horses died during the week of the Kentucky Derby, two of them in races in the hours leading up to the main event. Credit... Jon Cherry for The New York Times

Supported by

By Joe Drape and Melissa Hoppert

Joe Drape reported from Louisville, Ky., and Lexington, Ky., and Melissa Hoppert from New York.

• May 2, 2024

The Kentucky Derby has been run through two World Wars, the Great Depression, civil rights unrest and, most recently, a life-paralyzing pandemic. Now, on the 150th anniversary of America’s most famous race, the Sport of Kings faces another formidable foe: itself.

Last year, beneath Churchill Downs’s iconic twin spires, seven horses died during the week of the showpiece event — two of them in races in the hours leading up to the Derby. In the days after, five more sustained fatal injuries, prompting Churchill officials to move their races to another Kentucky racetrack.

It got worse. A colt trained by the sport’s most recognized and controversial trainer, Bob Baffert, died at Pimlico Race Course hours before Mr. Baffert saddled the winner of the Preakness Stakes, the second leg of the Triple Crown. Two more horses not trained by Mr. Baffert died in races surrounding the Belmont Stakes, the third leg, in June.

At the historic Saratoga Race Course in New York, 13 horses died while racing and training at the sport’s signature summer meet, including two who seemed poised to win their races before breaking down near the finish line on nationally televised broadcasts.

Over the past 12 months, The New York Times analyzed confidential documents and covert recordings made by law enforcement, and obtained exclusive interviews as part of an investigation into why so many horses, supposedly in peak physical condition, were breaking down so frequently. In the documentary “ The New York Times Presents: Broken Horses ,” now streaming on Hulu, The Times found that reckless breeding and doping practices, compromised veterinarians and trainers, and decades-long resistance to changes that could save horses lives have placed a multibillion-dollar ecosystem in peril and put the social acceptability of one of America’s oldest sports at risk.

“There’s a genuine feeling that this is the inflection point, and if we don’t act, it may be too late,” said Lisa Lazarus, the chief executive of the Horseracing Integrity and Safety Authority, or HISA, the federal agency that now regulates the sport.

In Louisville, Ky., on Saturday, racing officials and horse lovers will hold their collective breath and hope that every horse competing gets around the track safely. To avoid last year’s calamity, an army of veterinarians will pore over months of medical records with an assist from artificial intelligence and scrutinize horses each morning with the critical eye of a diamond jeweler. Data from high-tech motion sensors will monitor horses, and an old-fashioned “bucket brigade” as well as state-of-the-art equipment will be dispatched frequently to pick rocks from the racetrack that authorities determined could have played a part in last year’s cluster of deaths.

Saffie Joseph Jr., who was suspended by Churchill last year after two horses he trained collapsed and died ahead of the Derby, will have a horse in the race. He was reinstated when the necropsies of those horses were inconclusive.

“They were trying times,” Mr. Joseph said. “We let the process play out. We were cleared as we knew we would be.”

HISA investigated the deaths at Churchill and Saratoga and concluded that several factors, including frequency of high-intensity exercise, likely contributed. No illegal drugs were detected in the horses who died. The majority of the injuries involved a fetlock joint. Some of the horses who died received corticosteroid injections in their joints within 30 days of racing. That is currently allowed, although HISA has proposed prohibiting those injections within 30 days.

But racing’s problems go far beyond what happened last year. An F.B.I. investigation that began in 2015 produced nearly three years of wiretaps that provided a soundtrack for a deadly doping ring that stretched from Florida to New Jersey. At its center was a veterinarian and drug compounder named Dr. Seth Fishman, who bragged on wiretaps about “having a relationship with top trainers and top owners” in the horse racing world. He knew what he was doing and, in at least one case, wanted to make sure his clients understood that they were breaking the rules.

“What I’m trying to say is anytime you give something to a horse, that’s doping. So don’t kid yourself,” Dr. Fishman said to one, as heard in a wiretap.

The investigation exposed the weaknesses in American testing labs. After being tipped by an informant that some horses had recently been doped, an F.B.I. agent posing as a New Jersey racing official pulled samples from a group of horses and sent them to a Hong Kong laboratory considered one of the finest in the world. Evidence of illegal blood doping was detected.

The doping was often deadly. U.S. attorneys in the Southern District of New York said their three-year investigation had produced evidence that at least 20 horses perished because they were given illegal drugs by those involved in the ring.

“Nobody believed that anybody was going to jail for this behavior,” said Shaun Richards, the F.B.I. agent in charge of the investigation. But more than 30 trainers, veterinarians and drug salespeople either pleaded or were found guilty and went to jail.

One of those now in prison is the trainer Jason Servis , who in 2019 appeared to have won the Derby, but his horse, Maximum Security, was disqualified shortly after the race when officials determined that he interfered with other horses.

For the third straight year, the Derby will be run without a horse trained by Mr. Baffert. In 2021, his colt Medina Spirit won the Derby but subsequently was disqualified after testing positive for betamethasone, a potent corticosteroid used to reduce pain and inflammation. Churchill Downs barred him from its racetracks for two years and, over the summer, extended the suspension through 2024.

Mr. Baffert’s horses have won the Derby six times, and he has been named champion trainer four times. He is third on the career earnings list with more than $355 million in purses. Mr. Baffert also has a lengthy record of rule violations. According to regulators’ records, horses trained by him have failed 30 drug tests over four decades — most notably Medina Spirit, who died after a workout at a California racetrack five months after running the Derby. Since 2000, at least 77 horses have died under his care, according to data from the California Horse Racing Board.

“We decided to continue Bob Baffert’s suspension for another year because he hasn’t accepted responsibility for what happened,” Bill Carstanjen, chief executive of Churchill Downs Inc., said of the positive test in the Derby. “It’s about the game and the product as a whole, and it’s about ensuring to the public that they can rely on what they see being fair and safe. The rules have to apply to everybody.”

Mr. Baffert returned to the Triple Crown trail last year to win the Preakness Stakes with National Treasure in Baltimore. Hours before, however, another one of his colts, Havnameltdown, sustained a fatal injury during a race and was euthanized on the track.

The Times had two veterinarians, Dr. Sheila Lyons and Dr. Kate Papp, independently review the records related to the 2023 deaths at Churchill Downs and Pimlico. Dr. Lyons said the necropsies from Churchill were illuminating but incomplete because they lacked medication and treatment histories of each horse.

“What I found was that these horses had significant pre-existing injury, not only on the limb that broke down, but in other limbs as well,” Dr. Lyons said. “We don’t even know whether these horses were running with legal therapeutic medications.”

In the case of Havnameltdown, Dr. Lyons and Dr. Papp agreed that his death could have been prevented with vigilant veterinarian care by both his private veterinarian as well as regulatory ones in charge of ensuring a horse is sound before being allowed to race. Havnameltdown had lesions in each fetlock, which occur when the cartilage has worn away from repetitive injury.

“He didn’t only have it in the leg where this fracture occurred, this horse had it in all four limbs,” Dr. Lyons said. “This is easily diagnosed, X-ray equipment in every track practicing vet’s vehicle, it would take 10 minutes.”

Dr. Lyons said regulatory veterinarians noted abnormal findings in the colt’s range of motion and gait but ultimately concluded the horse was healthy enough to race. In addition, Havnameltdown had corticosteroids and hyaluronic acid — a pain reliever and an anti-inflammatory — injected in both hocks and both stifles a month before his last race. Joint injections are permitted by HISA up to 14 days before a race.

“Havnameltdown should not have been racing that day. Absolutely not, under any circumstances,” Dr. Papp said, based on her review of the necropsy results. “Baffert is the main caretaker for this horse. In my opinion, he is the responsible party for what happened.”

In an emailed statement, Mr. Baffert’s lawyer, Clark Brewster, said: “He entrusts the medical evaluation, diagnosis and treatment of the horses to his veterinarians and relies on their expertise. Baffert cares deeply for the horses under his care and is fully committed to their health, safety and general welfare.”

In August 2023, Mr. Baffert’s longtime veterinarian, Dr. Vince Baker, was placed on four years’ probation by the California Veterinary Medical Board for administering “dangerous drugs” to racehorses — including Medina Spirit — “at the request of their trainers without medical examinations or necessity.”

This will be the first Derby to fall under HISA’s antidoping and medication control program, which went into effect on May 22 — two days after Havnameltdown died. HISA has been tasked with enforcing uniform safety and medication rules in thoroughbred racing in the United States but has faced an uphill battle since it was established by Congress in 2020, taking over from state regulators.

Yet more than 50,000 samples were collected from 21,750 horses in 2023, resulting in 246 positive tests and the identification of 58 banned substances. The authority searched 141 barns across 38 tracks and recovered five different banned substances, resulting in 11 possession cases. An anonymous tip line received 122 calls, with more than 40 leading to an investigation.

“Are we ahead of the curve now? Probably not,” Ms. Lazarus said of being able to detect performance-enhancing drugs. “But we have a good chance at getting there.”

The National Thoroughbred Racing Association has acknowledged that horse racing has an image problem and recently started a multimillion-dollar advertising campaign called Safety Runs First that will be shown throughout the Triple Crown.

One change that HISA celebrated was its use of six drug-testing laboratories to deliver uniformity and faster turnaround times. The University of Kentucky’s Equine Analytical Chemistry Laboratory, however, was recently removed because of alleged personnel and quality issues. The university and HISA would not comment while investigations are underway.

The rate of fatal injury increased slightly in 2023, to 1.32 per 1,000 starts, from 1.25 in 2022, which was the lowest rate since 2009, when the Jockey Club started the database. HISA said that racetracks under its jurisdiction had 1.23 fatalities per 1,000 starts. (Texas, Louisiana, West Virginia and Nebraska have pushed back against HISA regulation and are not covered.) Neither data set includes training fatalities.

Ms. Lazarus said that by 2025, the authority hoped to have a public database that logged racing and training fatalities as they happened, like the ones kept by California and New York. She also said HISA was working to standardize necropsy procedures.

She acknowledges there are limits to HISA’s authority, which covers horses that have recorded a timed workout at the racetrack. Breeding and sales remain largely unregulated, and practices like repeated breeding of unsound horses, corrective surgeries and drug use are believed to be widespread. The three major thoroughbred sales companies recently announced that starting July 1 they will strengthen their drug policy to more closely align with HISA’s. Yet the enforcement of such a policy would be up to the companies, and no details have been provided.

Arthur Hancock III, who along with his wife, Staci, has campaigned for reform since the 1990s, says the authority must succeed. In 2013, the couple formed the Water Hay Oats Alliance to get drugs out of racing, growing it to more than 1,800 industry members who shamed horsemen, veterinarians, politicians and regulators into treating thoroughbreds as athletes rather than commodities.

“There is a new sheriff in town, and he means business,” Mr. Hancock, a fourth-generation breeder, said of HISA. “If we don’t get rid of the drugs and thugs, they’re going to get rid of us.”

Joe Drape is a Times reporter writing about how the intersection of money, power and sports impacts our culture. More about Joe Drape

Melissa Hoppert , a deputy editor for live coverage, joined The Times in 2006. She helped create the horse racing blog The Rail and has directed coverage of the N.F.L. and college sports. More about Melissa Hoppert

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