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Eureka Math Student Materials: Grades K–5

Learn, Practice, Succeed

Learn, Practice, and Succeed from   Eureka Math™   offer teachers multiple ways to differentiate instruction, provide extra practice, and assess student learning. These versatile companions to   A Story of Units®   (Grades K–5) guide teachers in response to intervention (RTI), provide extra practice, and inform instruction.

Also available for Grades 6–8 . 

Learn, Practice, Succeed can be purchased all together or bundled in any configuration. Contact your account solutions manager for more information and pricing.  

The Learn book serves as a student’s in-class companion where they show their thinking, share what they know, and watch their knowledge build every day!

Application Problems:  Problem solving in a real-world context is a daily part of   Eureka Math , building student confidence and perseverance as students apply their knowledge in new and varied ways.

Problem Sets :  A carefully sequenced Problem Set provides an in-class opportunity for independent work, with multiple entry points for differentiation.

Exit Tickets:   These exercises check student understanding, providing the teacher with immediate, valuable evidence of the efficacy of that day’s instruction and informing next steps.

Templates:   Learn   includes templates for the pictures, reusable models, and data sets that students need for   Eureka Math   activities.

With   Practice , students build competence in newly acquired skills and reinforce previously learned skills in preparation for tomorrow’s lesson.   Together,   Learn   and   Practice   provide all the print materials a student uses for their core instruction.

Eureka Math  contains multiple daily opportunities to build fluency in   mathematics . Each is designed with the same notion—growing every student’s ability to use mathematics   with ease . Fluency experiences are generally fast-paced and energetic, celebrating improvement and focusing on recognizing patterns and connections within the material.

Eureka Math   fluency activities provide differentiated practice through a variety of formats—some are conducted orally, some use manipulatives, others use a personal whiteboard, or a handout and paper-and-pencil format.

Sprints:  Sprint fluency activities in  Eureka Math Practice  build speed and accuracy with already acquired skills. Used when students are nearing optimum proficiency, Sprints leverage tempo to build a low-stakes adrenaline boost that increases memory and recall. Their intentional design makes Sprints inherently differentiated – the problems build from simple to complex, with the first quadrant of problems being the simplest, and each subsequent quadrant adding complexity.

Eureka Math Succeed   enables students to work individually toward mastery.  Teachers and tutors can use  Succeed   books from prior grade levels as curriculum-consistent tools for filling gaps in foundational knowledge. Students will thrive and progress more quickly, as familiar models facilitate connections to their current, grade-level content.

Additional Problem Sets:  Ideal for Homework or extra practice, these additional problem sets align lesson-by-lesson with what is happening in the classroom. These problems are sequenced from simple-to-complex to naturally scaffold student practice. They align with   Eureka Math   and use the curriculum’s mathematical models and language, ensuring that students feel the connections and relevance to their daily instruction, whether they are working on foundational skills or getting extra practice on the current topic.

Homework Helpers:   Each problem set is accompanied by a Homework Helper, a set of worked examples that illustrate how similar problems are solved. The examples, viewed side by side with the homework, support students as they reinforce the day’s learning. Homework Helpers are also a great way to keep parents informed about math class.

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Eureka Math Grade 3 Module 3 Lesson 12 Answer Key

Students of Grade 3 can get a strong foundation by referring to the Eureka Math Book. It was developed by highly professional mathematics educators and the solutions prepared by them are in a concise manner for easy grasping. To achieve high scores in Grade 3, students need to solve all questions and exercises included in Eureka Grade 3 Book.

Engage NY Eureka Math 3rd Grade Module 3 Lesson 12 Answer Key

Teachers and students can find this Eureka Book Answer Key for Grade 3 more helpful in raising students’ scores and supporting teachers to educate the students. Learning activities are the best option to educate elementary school kids and make them understand the basic mathematical concepts like addition, subtraction, multiplication, division, etc. Grade 3 elementary school students can find these fun-learning exercises for all math concepts through the Eureka Book.

Eureka Math Grade 3 Module 3 Lesson 12 Pattern Sheet Answer Key

Answer: 8 x 1 = 8, 8 x 2 = 16, 8 x 3 = 24, 8 x 5 = 40, 8 x 6 = 48, 8 x 7 = 56, 8 x 8 = 64, 8 x 9 = 72, 8 x 10 = 80, 8 x 5 = 40, 8 x 6 = 48, 8 x 5 = 40, 8 x 7 = 56, 8 x 5 = 40, 8 x 6 = 48, 8 x 5 = 40, 8 x 7 = 56, 8 x 5 = 40, 8 x 8 = 64, 8 x 5 = 40, 8 x 9 = 72, 8 x 5 = 40, 8 x 10 = 80, 8 x 6 = 48, 8 x 5 = 40, 8 x 6 = 48, 8 x 7 = 56, 8 x 6 = 48, 8 x 8 = 64, 8 x 6 = 48, 8 x 9 = 72, 8 x 6 = 48, 8 x 7 = 56, 8 x 6 = 48, 8 x 7 = 56, 8 x 8 = 64, 8 x 7 = 56, 8 x 9 = 72, 8 x 7 = 56, 8 x 8 = 64, 8 x 6 48, 8 x 8 = 64, 8 x 7 = 56, 8 x 8 = 64, 8 x 9 = 72, 8 x 9 = 72, 8 x 6 = 48, 8 x 9 = 72, 8 x 7 = 56, 8 x 9 = 72, 8 x 8 = 64, 8 x 9 = 72, 8 x 8 = 64, 8 x 6 = 48, 8 x 9 = 72, 8 x 7 = 56, 8 x 9 = 72, 8 x 6 = 48, 8 x 8 = 64, 8 x 9 = 72, 8 x 7 = 56, 8 x 6 = 48, 8 x 8 = 64.

Eureka Math Grade 3 Module 3 Lesson 12 Problem Set Answer Key

Answer: 6 x 9 = 54.

Answer: 7 x 9 = 63.

Answer: 8 x 9 = 72.

Answer: 9 x 9 = 81.

Question 2. Find the total value of the shaded blocks.

Answer: 9 x 6 = 54.

Explanation: In the above-given equation, given that, 9 sixes = 10 sixes – 1 six. 60 – 6. 54.

Answer: 9 x 7 = 63.

Explanation: In the above-given equation, given that, 9 sevens = 10 sevens – 1 seven. 70 – 7. 63.

Answer: 9 x 8 = 72.

Explanation: In the above-given equation, given that, 9 eights = 10 eights – 1 eight. 80 – 8. 72.

Explanation: In the above-given equation, given that, 9 nines = 10 nines – 1 nine. 90 – 9. 81.

Question 3. Matt buys a pack of postage stamps. He counts 9 rows of 4 stamps. He thinks of 10 fours to find the total number of stamps. Show the strategy that Matt might have used to find the total number of stamps.

Answer: 9 x 4 = 36.

Explanation: In the above-given equation, given that, 9 fours = 10 fourss – 1 four. 40 – 4. 36.

Answer: 3 x 9 = 27, 45 / 9 = 5. 9 x 9 = 81, 9 / 9 = 1. 8 x 9 = 72, 90 / 9 = 10. 9 x 4 = 36, 72 / 9 = 8. 2 x 9 = 18, 54 / 9 = 6.

Eureka Math Grade 3 Module 3 Lesson 12 Exit Ticket Answer Key

Explanation: In the above-given question, given that, 5 x 9 = ( 5 + 1 ) x 9. ( 5 x 9 ) + ( 1 x 9 ) 45 + 9. 54.

Question 2. Hector solves 9 × 8 by subtracting 1 eight from 10 eights. Draw a model, and explain Hector’s strategy.

Explanation: In the above-given question, given that, 9 x 8 = 72. 10 eights – 1 eight. 80 – 8. 72.

Eureka Math Grade 3 Module 3 Lesson 12 Homework Answer Key

Question 1. Find the value of each row. Then, add the rows to find the total.

Explanation: In the above-given question, given that, the multiplication and division of 9 is given. 50 – 5 = 45, 9 x 5 = 45. 60 – 6 = 54, 9 x 6 = 54. 70 – 7 = 63, 9 x 7 = 63. 80 – 8 = 72, 9 x 8 = 72. 90 – 9 = 81, 9 x 9 = 81. 40 – 4 = 36, 9 x 4 = 36.

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Break Apart Ones to Add - Lesson 4.1

Group Tens as Hundreds - Lesson 2.1

Explore 3 Digit Numbers - Lesson 2.2

Model 3 Digit Numbers - Lesson 2.3

Hundreds, Tens, and Hundreds - Lesson 2.4

​Place Value to 1,000 - Lesson 2.5

​ Number Names - Lesson 2.6

Different Forms of Numbers - Lesson 2.7

Algebra - Different Ways to Show Numbers - 2.8

Count On and Count Back by 10 and 100 - 2.9

Algebra - Number Patterns - Lesson 2.10

​Problem Solving - Compare Numbers - Lesson 2.11

Algebra - Compare Numbers - Lesson 2.12

​Chapter 2 Review for Test - Numbers to 1,000

Draw to Represent 3-Digit Addition - Lesson 6.1

Break Apart 3-Digit Addends - Lesson 6.2

3-Digit Addition - Regrouping Ones - Lesson 6.3

3-Digit Addition - Regrouping Tens - Lesson 6.4

​3-Digit Addition - Regroup Ones and Tens - L. 6.5

Problem Solving: 3-Digit Subtraction - Lesson 6.6

3-Digit Subtraction: Regroup Tens - Lesson 6.7

3-Digit Subtraction: Regroup Hundreds - Lesson 6.8

Subtraction: Regroup Ones and Tens - Lesson 6.9

Use Double Facts - Lesson 3.1 ​

Practice Addition Facts - Lesson 3.2

Algebra - Make a Ten to Add - Lesson 3.3

Algebra - Add 3 Addends - Lesson 3.4

Algebra - Relate Addition and Subtraction - Lesson 3.5

Practice Subtraction Facts - Lesson 3.6

Use Ten to Subtract - Lesson 3.7

Algebra - Use Drawings to Represent Problems - L. 3.8

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Problem Solving - Equal Groups - Lesson 3.10

Second Grade

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Dimes, Nickels, and Pennies - Lesson 7.1

Quarters - Lesson 7.2

Count Collections - Lesson 7.3

​ Show Amounts in Two Ways - Lesson 7.4

One Dollar - Lesson 7.5

Amounts Greater than $1 - Lesson 7.6

​ Problem Solving With Money - Lesson 7.7

Lesson 1.1 - Even and Odd Numbers

Lesson 1.2 - Representing Even Numbers

​Lesson 1.3 - Understanding Place Value

Lesson 1.4 - Expanded Form

Lesson 1.5 - Different Ways to Write Numbers

Lesson 1.6 - Different Names for Numbers

Lesson 1.7 - Problem Solving - Tens and Ones

Lesson 1.8 - Counting Patterns Within 100

Lesson 1.9 - Counting Patterns Within 1000

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Elimination (Lesson 2.3)

Unit 1: sequences and linear functions, day 1: recursive sequences, day 2: applications of arithmetic sequences, day 3: sum of an arithmetic sequence, day 4: applications of geometric sequences, day 5: sequences review, day 6: quiz 1.1 to 1.4, day 7: linear relationships, day 8: point-slope form of a line, day 9: standard form of a linear equation, day 10: quiz 1.5 to 1.7, day 11: unit 1 review, day 12: unit 1 test, unit 2: linear systems, day 1: linear systems, day 2: number of solutions, day 3: elimination, day 4: larger systems of equations, day 5: quiz 2.1 to 2.4, day 6: systems of inequalities, day 7: optimization using systems of inequalities, day 8: quiz 2.5 to 2.6, day 9: unit 2 review, day 10: unit 2 test, unit 3: function families and transformations, day 1: interpreting graphs, day 2: what is a function, day 3: translating functions, day 4: quiz 3.1 to 3.3, day 5: quadratic functions and translations, day 6: square root functions and reflections, day 7: absolute value functions and dilations, day 8: equations of circles, day 9: quiz 3.4 to 3.7, day 10: unit 3 review, day 11: unit 3 test, unit 4: working with functions, day 1: using multiple strategies to solve equations, day 2: solving equations, day 3: solving nonlinear systems, day 4: quiz 4.1 to 4.3, day 5: combining functions, day 6: composition of functions, day 7: inverse relationships, day 8: graphs of inverses, day 9: quiz 4.4 to 4.7, day 10: unit 4 review, day 11: unit 4 test, unit 5: exponential functions and logarithms, day 1: writing exponential functions, day 2: graphs of exponential functions, day 3: applications of exponential functions, day 4: quiz 5.1 to 5.3, day 5: building exponential models, day 6: logarithms, day 7: graphs of logarithmic functions, day 8: quiz 5.4 to 5.6, day 9: unit 5 review, day 10: unit 5 test, unit 6: quadratics, day 1: forms of quadratic equations, day 2: writing equations for quadratic functions, day 3: factoring quadratics, day 4: factoring quadratics. part 2., day 5: solving using the zero product property, day 6: quiz 6.1 to 6.4, day 7: completing the square, day 8: completing the square for circles, day 9: quadratic formula, day 10: complex numbers, day 11: the discriminant and types of solutions, day 12: quiz 6.5 to 6.9, day 13: unit 6 review, day 14: unit 6 test, unit 7: higher degree functions, day 1: what is a polynomial, day 2: forms of polynomial equations, day 3: polynomial function behavior, day 4: repeating zeros, day 5: quiz 7.1 to 7.4, day 6: multiplying and dividing polynomials, day 7: factoring polynomials, day 8: solving polynomials, day 9: quiz 7.5 to 7.7, day 10: unit 7 review, day 11: unit 7 test, unit 8: rational functions, day 1: intro to rational functions, day 2: graphs of rational functions, day 3: key features of graphs of rational functions, day 4: quiz 8.1 to 8.3, day 5: adding and subtracting rational functions, day 6: multiplying and dividing rational functions, day 7: solving rational functions, day 8: quiz 8.4 to 8.6, day 9: unit 8 review, day 10: unit 8 test, unit 9: trigonometry, day 1: right triangle trigonometry, day 2: solving for missing sides using trig ratios, day 3: inverse trig functions for missing angles, day 4: quiz 9.1 to 9.3, day 5: special right triangles, day 6: angles on the coordinate plane, day 7: the unit circle, day 8: quiz 9.4 to 9.6, day 9: radians, day 10: radians and the unit circle, day 11: arc length and area of a sector, day 12: quiz 9.7 to 9.9, day 13: unit 9 review, day 14: unit 9 test, learning targets.

Solve linear systems using elimination.

Use elimination strategies to determine if a system has 0, 1, or infinite solutions.

Activity: How Much is a Taco?

Lesson handouts, media locked.

Our Teaching Philosophy:

Experience first, formalize later (effl), experience first.

The goal of this lesson is that students use their problem solving skills to solve linear systems without a step-by-step procedure. Instead we want them thinking about how would they actually figure this out if they were Jacob or Amala. The questions were written with that in mind. It is our hope that students won't jump to graphing in their calculators or to solving with substitution. While they could do that, this system is actually much faster to solve without those methods, which is one of the reasons we like elimination. Sometimes it's a lot simpler than other methods.

So as students are working, keep in mind that we are trying to get them to see what the simplest way to solve is. Question 2b really gets at this. What are the differences in the orders? Ask students, "What more did Jacob and Amala get? How much more did they pay?"

Question 3 is going to be tougher for students. We want them to notice that they can double or triple Amala's order so that she has the same number of slices or cannolis as Jacob. So how do we get them to see that? You'll want to be ready with your guiding questions. Also, multiple groups may have this same question so trying to help a couple groups at a time can keep the class moving.

Guiding Questions:

• Why was I able to solve for the burritos before?
• How is this set up different from the last?
• Amala didn't buy the same number of slices as Jacob, but could we rewrite her equation so that it also contains 3 slices?

Formalize Later

The margin notes for this lesson are really cool because we're actually going to take the students work and show how the elimination works algebraically in the margin. So in question 1, when we ask about the differences in the orders, we're going to show how that is taking one equation and subtracting the other. That leaves us with an equation that we can solve because now we have one resulting equation with one variable. Now that we know one variable, we can solve for the other.

As you're debriefing the rest of the activity, try to highlight as many different approaches as possible. You may even ask multiple groups to write their solutions to the same problem on the board if they solved it in a different way. For example, some students might solve question 3c by eliminating the slices of pizza while others may have eliminated the cannolis.

One last thing...the last Check Your Understanding problem is modeled after a practice SAT item. These types of questions are VERY common on the SAT, and while students could find the correct answer by plugging in an answer choice and solving the system, they will save a lot of time if they notice the structure in the system and that we want coefficients that are multiples of each other.

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Home > CC2 > Chapter 5 > Lesson 5.3.2

Lesson 5.1.1, lesson 5.1.2, lesson 5.2.1, lesson 5.2.2, lesson 5.2.3, lesson 5.2.4, lesson 5.2.5, lesson 5.2.6, lesson 5.3.1, lesson 5.3.2, lesson 5.3.3, lesson 5.3.4, lesson 5.3.5.

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