illustrative math grade 3 homework

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Grade 3 math tasks from Illustrative Math

This collection includes a variety of content and practice standard based math tasks for 3rd grade students. Illustrative Mathematics has been providing instructional and assessment tasks, lesson plans, and other resources for teachers, assessment writers, and curriculum developers since 2011. 

Please note that the files in this collection can not be downloaded from WeTeachNYC because they link out to an external site. Scroll down to find links to Illustrative Mathematics content.

Included Resources

Addition patterns.

This task asks students to study some patterns in a small addition table. From Illustrative Mathematics.

Rounding to 50 or 500

This task poses a series of questions teachers might use to instruct or assess understanding of rounding to the nearest ten and hundred. From Illustrative Mathematics.

Which is closer to 1?

This task poses a multi-step problem to 3rd graders who have  some expertise with fractions already. This task can be used to assess students' current understanding of fractions smaller and larger than one. This task also lists other tasks that lead up to this task, if you're beginning to teach fractions or reteaching some concepts. From Illustrative Mathematics.

Halves, thirds, and sixths

Students explore area, recognize different ways of representing fractions with area, and understand why fractions are equivalent in special cases.  From Illustrative Mathematics.

Introducing the distributive property

Introducing the distributive p....

 This instructional task is best used when students are first working with the distributive property.  From Illustrative Mathematics.

Shapes and their insides

The purpose of this task is to help students differentiate between a polygon and the region inside of a polygon. From Illustrative Mathematics.

How many colored pencils?

The purpose of this task is to support students' reasoning based on place value to multiply a single digit number by a multiple of 10. If used in an instructional setting, students might benefit from having access to base-ten blocks. Students should also be encouraged to use a number line marked with tens. From Illustrative Mathematics.

Classroom supplies

Students solve problems involving the four operations,and draw scaled graphs with the task. From Illustrative Mathematics.

The class trip

Students solve a two-step word problem and represent an unknown quantity with a variable in this task. From Illustrative Mathematics.

Dajuana's homework: Elapsed time questions

Dajuana's homework: elapsed ti....

The purpose of this task is for students to work on elapsed-time questions. This task includes three different elapsed time situations: end-time unknown, elapsed time unknown, and start-time unknown. From Illustrative Mathematics.

3rd grade math task collection highlights

3rd grade math task collection....

This document shares an overview of the WeTeachNYC collection of 3rd grade math tasks from Illustrative Math.

IM 6–12 Math: Grading and Homework Policies and Practices

By Jennifer Willson,  Director, 6–12 Professional Learning Design

In my role at IM, working with teachers and administrators, I am asked to help with the challenges of implementing an IM curriculum. One of the most common challenges is: how can we best align these materials to our homework and grading practices? This question is a bit different from “How should we assess student learning?” or “How should we use assessment to inform instruction?” 

When we created the curriculum, we chose not to prescribe homework assignments or decide which student work should count as a graded event. This was deliberate—homework policies and grading practices are highly variable, localized, and values-driven shared understandings that evolve over time. For example, the curriculum needed to work for schools where nightly, graded assignments are expected; schools where no work done outside of class is graded; and schools who take a feedback-only approach for any formative work.

IM 6–8 Math was released in 2017, and IM Algebra 1, Geometry, and Algebra 2 in 2019. In that time, I’ve been able to observe some patterns in the ways schools and teachers align the materials to their local practices. So, while we’re still not going to tell you what to do, we’re now in a position to describe some trends and common ways in which schools and districts make use of the materials to meet their local constraints. Over the past four years, I have heard ideas from teachers, administrators, and IM certified facilitators. In December, I invited our IM community to respond to a survey to share grading and homework policies and practices. In this post I am sharing a compilation of results from the 31 teachers who responded to the survey, as well as ideas from conversations with teachers and IMCFs. We hope that you find some ideas here to inform and inspire your classroom.

How do teachers collect student responses?

Most teachers who responded to the survey collect student work for assessments in a digital platform such as LearnZillion, McGraw-Hill, ASSISTments, Edulastic, Desmos, etc. Others have students upload their work (photo, PDF, etc.) to a learning management system such as Canvas or Google classroom. Even fewer ask students to respond digitally to questions in their learning management system.

How do teachers tend to score each type of assessment, and how is feedback given?

The table shows a summary of how teachers who responded to the survey most often provide feedback for the types of assessments included in the curriculum.

How are practice problems used?

Every lesson in the curriculum (with a very small number of exceptions) includes a short set of cumulative practice problems. Each set could be used as an assignment done in class after the lesson or worked on outside of class, but teachers make use of these items in a variety of ways to meet their students’ learning needs.

While some teachers use the practice problems that are attached to each lesson as homework, others do not assign work outside of class. Here are some other purposes for which teachers use the practice problems:

• extra practice
• student reflection
• as examples to discuss in class or use for a mini-lesson
• as a warm-up question to begin class
• as group work during class

How do teachers structure time and communication to “go over” practice problems?

It’s common practice to assemble practice problems into assignments that are worked on outside of class meeting time. Figuring out what works best for students to get feedback on practice problems while continuing to move students forward in their learning and work through the next lesson can be challenging. 

Here are some ways teachers describe how they approach this need:

• We don’t have time to go over homework every day, but I do build in one class period per section to pause and look at some common errors in cool-downs and invite students to do some revisions where necessary, then I also invite students to look at select practice problems. I collect some practice problems along with cool-downs and use that data to inform what, if anything, I address with the whole class or with a small group.
• Students vote for one practice problem that they thought was challenging, and we spend less than five minutes to get them started. We don’t necessarily work through the whole problem.
• I post solutions to practice problems, sometimes with a video of my solution strategy, so that students can check their work.
• I assign practice problems, post answers, invite students to ask questions (they email me or let me know during the warm-up), and then give section quizzes that are closely aligned to the practice problems, which is teaching my students that asking questions is important.
• I invite students to vote on the most challenging problem and then rather than go over the practice problem I weave it into the current day’s lesson so that students recognize “that’s just like that practice problem!” What I find important is moving students to take responsibility to evaluate their own understanding of the practice problems and not depend on me (the teacher) or someone else to check them. Because my district requires evidence of a quiz and grade each week and I preferred to use my cool-downs formatively, I placed the four most highly requested class practice problems from the previous week on the quiz which I substituted for that day’s cool-down. That saved me quiz design time, there were no surprises for the students, and after about four weeks of consistency with this norm, the students quickly learned that they should not pass up their opportunity to study for the quiz by not only completing the 4–5 practice problems nightly during the week, but again, by reflecting on their own depth of understanding and being ready to give me focused feedback about their greatest struggle on a daily basis.
• I see the practice problems as an opportunity to allow students to go at different paces. It’s more work, but I include extension problems and answers to each practice problem with different strategies and misconceptions underneath. When students are in-person for class, they work independently or in pairs moving to the printed answer keys posted around the room for each problem. They initial under different prompts on the answer key (tried more than one strategy, used a DNL, used a table, made a mistake, used accurate units, used a strategy that’s not on here…) It gives the students and I more feedback when I collect the responses later and allows me to be more present with smaller groups while students take responsibility for checking their work. It also gets students up and moving around the room and normalizes multiple approaches as well as making mistakes as part of the problem solving process.

Quizzes—How often, and how are they made?

Most of the teachers give quizzes—a short graded assessment completed individually under more controlled conditions than other assignments. How often is as varied as the number of teachers who responded: one per unit, twice per unit, once a week, two times per week, 2–3 times per quarter.

If teachers don’t write quiz items themselves or with their team, the quiz items come from practice problems, activities, and adapted cool-downs.

When and how do students revise their work?

Policies for revising work are also as varied as the number of teachers who responded. 

Here are some examples:

• Students are given feedback as they complete activities and revise based on their feedback.
• Students revise cool-downs and practice problems.
• Students can revise end-of-unit assessments and cool-downs.
• Students can meet with me at any time to increase a score on previous work.
• Students revise cool-downs if incorrect, and they are encouraged to ask for help if they can’t figure out their own error.
• Students can revise graded assignments during office hours to ensure successful completion of learning goals.
• Students are given a chance to redo assignments after I work with them individually.
• Students can review and revise their Desmos activities until they are graded.
• We make our own retake versions of the assessments.
• Students can do error logs and retakes on summative assessments.
• We complete the student facing tasks together as a whole class on Zoom in ASSISTments. If a student needs to revise the answers they notify me during the session.

Other advice and words of wisdom

I also asked survey participants for any other strategies that both have and haven’t worked in their classrooms. Here are some responses.

What have you tried that has not worked?

• Going over practice problems with the whole class every day. The ones who need it most often don’t benefit from the whole-class instruction, and the ones who don’t need it distract those who do. 
• Grading work on the tasks within the lessons for accuracy
• Leaving assignments open for the length of the semester so that students can always see unfinished work
• Going through problems on the board with the whole class does not correct student errors
• Most students don’t check feedback comments unless you look at them together
• Grading images of student work on the classroom activity tasks uploaded by students in our learning management systems
• Providing individual feedback on google classroom assignments was time consuming and inefficient
• Allowing students to submit late and missing work with no penalty
• Trying to grade everything
• Below grade 9, homework really does not work.
• Going over every practice problem communicates that students do not really think about the practice problems on their own. 

What else have you tried that has worked well?

• My students do best when I consistently assign practice problems. I have tried giving them an assignment once a week but most students lose track. It is better to give 2–3 problems or reflective prompts after every class, which also helps me get ahead of misconceptions.
• I don’t grade homework since I am unsure who completes it with or for the students.
• A minimum score of 50% on assignments, which allows students the opportunity to recover, in terms of their grade in the class
• Time constraints imposed during remote learning impact the amount and type of homework I give as well as what I grade
• Give fewer problems than normal on second chance assignments
• I have used platforms such as Kahoot to engage students in IM material. I also build Google Forms to administer the Check Your Readiness pre-assessment and End-of-Unit assessments, but I may start using ASSISTments for this in the future.
• The value of homework in high school is okay, but personally I skip good for great.
• Students are able to go back and revise their independent practice work upon recognizing their mistakes and learning further about how to solve the problems.
• Sometimes I select only one or two slides to grade instead of the whole set when I use Desmos activities.
• Allow for flexibility in timing. Give students opportunities for revision.
• Frequent short assessments are better than longer tests, and they allow students to focus on specific skills and get feedback more frequently.
• Especially during the pandemic, many of my students are overwhelmed and underachieving. I am focusing on the core content.
• Homework assignments consist of completing Desmos activities students began in class. Additional slides contain IM practice problems.
• I am only grading the summative assessment for accuracy and all else for completion. I want the students to know that they have the room to learn, try new strategies and be wrong while working on formative assessments.

What grading and homework policies have worked for you and your students that aren’t listed? Share your ideas in the comments so that we can all learn from your experience.

What would you like to learn more about? Let us know in the comments, and it will help us design future efforts like this one so that we can all learn more in a future blog post.

We are grateful to the teachers and facilitators who took the time to share their learning with us.

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Engage your students with effective distance learning resources. ACCESS RESOURCES>>

3.oa. grade 3 - operations and algebraic thinking, 3.oa.a. represent and solve problems involving multiplication and division., 3.oa.a.1. interpret products of whole numbers, e.g., interpret $5 \times 7$ as the total number of objects in 5 groups of 7 objects each. for example, describe a context in which a total number of objects can be expressed as $5 \times 7$..

• No tasks yet illustrate this standard.

3.OA.A.2. Interpret whole-number quotients of whole numbers, e.g., interpret $56 \div 8$ as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as $56 \div 8$.

• Markers in Boxes

3.OA.A.3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. See Glossary, Table 2.

• Analyzing Word Problems Involving Multiplication
• Classroom Supplies
• Gifts from Grandma, Variation 1
• Two Interpretations of Division

3.OA.A.4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations $8 \times ? = 48$, $5 = \boxvoid \div 3$, $6 \times 6 = ?$

• Finding the unknown in a division equation

3.OA.B. Understand properties of multiplication and the relationship between multiplication and division.

3.oa.b.5. apply properties of operations as strategies to multiply and divide. students need not use formal terms for these properties. examples: if $6 \times 4 = 24$ is known, then $4 \times 6 = 24$ is also known. (commutative property of multiplication.) $3 \times 5 \times 2$ can be found by $3 \times 5 = 15$, then $15 \times 2 = 30$, or by $5 \times 2 = 10$, then $3 \times 10 = 30$. (associative property of multiplication.) knowing that $8 \times 5 = 40$ and $8 \times 2 = 16$, one can find $8 \times 7$ as $8 \times (5 + 2) = (8 \times 5) + (8 \times 2) = 40 + 16 = 56$. (distributive property.).

• Valid Equalities? (Part 2)

3.OA.B.6. Understand division as an unknown-factor problem. For example, find $32 \div 8$ by finding the number that makes $32$ when multiplied by $8$.

3.oa.c. multiply and divide within 100., 3.oa.c.7. fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that $8 \times 5 = 40$, one knows $40 \div 5 = 8$) or properties of operations. by the end of grade 3, know from memory all products of two one-digit numbers..

• Kiri's Multiplication Matching Game

3.OA.D. Solve problems involving the four operations, and identify and explain patterns in arithmetic.

3.oa.d.8. solve two-step word problems using the four operations. represent these problems using equations with a letter standing for the unknown quantity. assess the reasonableness of answers using mental computation and estimation strategies including rounding. this standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (order of operations)..

• The Class Trip
• The Stamp Collection

3.OA.D.9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

• Addition Patterns
• Making a ten
• Patterns in the multiplication table
• Symmetry of the addition table

• Math Curriculum
• Professional Learning

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An Assortment of Fractions

Lesson Purpose

Lesson narrative.

In a previous unit, students learned to recognize and generate equivalent fractions. Earlier in this unit, they learned to add and subtract fractions with the same denominator, seeing these operations as joining and separating parts of the same whole. In this lesson, students encounter situations that involve combining and removing fractions with different denominators (limited to 2, 3, 4, 6, and 8), prompting them to rely on their understanding about equivalence to reason about the problems. This work prepares students to use equivalent fractions to join tenths and hundredths in upcoming lessons.

Students are not expected to reason symbolically, or to write fractional expressions with different denominators and then rewrite them with a common denominator. Instead, they reason using their intuitive understanding of equivalence, which they have begun to build since grade 3, and with the support of visual representations as needed.

Activity 2: Stacks of Blocks

Learning Goals

Teacher Facing

• Use equivalence to reason about addition and subtraction problems.

Student Facing

• Let’s find the heights of some stacked objects.

Required Preparation

Ccss standards.

Building On

Building Towards

Lesson Timeline

Teacher reflection questions, suggested centers.

• Jump the Line (2–5), Stage 2: Add and Subtract Tenths and Hundredths (Addressing)
• Compare (1–5), Stage 6: Add and Subtract Fractions (Addressing)

Print Formatted Materials

For access, consult one of our IM Certified Partners .

Additional Resources

Unit 3 Family Materials

Multiplying and dividing fractions.

In this unit, students use area concepts to represent and solve problems involving the multiplication of two fractions, and generalize that when they multiply two fractions, they need to multiply the two numerators and the two denominators to find their product. They also reason about the relationship between multiplication and division to divide a whole number by a unit fraction and a unit fraction by a whole number.

Section A: Fraction Multiplication

In this section, students build on their knowledge of fraction multiplication developed in the previous unit by using area concepts to understand the multiplication of a fraction times a fraction. Students draw diagrams to represent the fractional area. For example, students learn that the diagrams below can represent the situation “Kiran eats macaroni and cheese from a pan that is \(\frac {1}{3}\) full. He eats \(\frac {1}{4}\) of the remaining macaroni and cheese in the pan. How much of the whole pan did Kiran eat?”

pan with \(\frac{1}{3} \) left

eat \(\frac{1}{4}\)  of what’s left

\(\frac{1}{4}\) of \(\frac{1}{3}\) is \(\frac{1}{12}\)

Students extend this conceptual understanding to multiply all types of fractions including fractions greater than 1 (for example,  \(\frac{7}{4}\) ). In each case, the students relate this multiplication to finding the area of a rectangle with fractions as side lengths. As the lessons progress, they notice that they can multiply the two numerators and the two denominators to find their product. This reasoning holds true for fractions greater than 1. For example, \(\frac{3}{4}\times\frac{7}{5}=\frac{3\times 7}{4\times5}=\frac{21}{20}\) .

Section B: Fraction Division

The section begins by using whole numbers to recall that the size of the quotient depends, for example, on the amount being shared and the number of people sharing. That is, each student will get more pretzels if 3 students share 45 pretzels than if 3 students share 24 pretzels. Similarly, each student will get fewer pretzels if 6 students share 24 pretzels than if 3 students share 24 pretzels.

This thinking helps students understand why dividing a whole number by a unit fraction results in a quotient that is larger than the whole number. For example, \(2 \div \frac{1}{3} = 6\) because there are 6 groups of  \(\frac{1}{3}\) in 2. As students draw diagrams and write expressions involving the division of unit fractions, students recognize the relationship between multiplication and division. For example, they may notice that \(2 \div \frac{1}{3} = 6\) because \(6 \times \frac{1}{3} = 2\) , and that \(\frac{1}{5} \div 2 = \frac {1}{10}\) is related  to \(2 \times \frac{1}{10} = \frac {1}{5}\) .

Section C: Problem Solving with Fractions

In this section, students apply what they have learned in the previous sections through problem solving. Students see how fraction multiplication and division are useful in different contexts. They use the meaning of multiplication and division to decide which operation to use to solve various problems. As students share strategies, they may realize that some problems could be solved using either division or multiplication.

Try it at home!

Near the end of the unit, ask your student to solve the following question:

A painter was painting a wall yellow. He painted \(\frac{1}{3}\) of the wall yellow before being told he needed to paint the wall blue. At the end of the day, he was able to cover up \(\frac{1}{5}\) of the yellow wall in blue. How much of the entire wall is blue?

Questions that may be helpful as they work:

• Can you draw a diagram to help you solve the problem?
• What equation would you use to solve the problem?
• Can you solve this using division or multiplication instead?

Illustrative Math: 4th Grade Unit 8 - Full Unit Homework/Practice

Products in this Bundle (2)

Description.

This product is an excellent resource for independent practice for Illustrative Mathematics. It provides students with extra practice for 4th Grade IM Unit 8, which can be used as homework or practice. It will help students to:

• Students classify triangles and quadrilaterals based on the properties of their side lengths and angles, and learn about lines of symmetry in two-dimensional figures. They use their understanding of these attributes to solve problems, including problems involving perimeter and area.
• Classify triangles (including right triangles), parallelograms, rectangles, rhombuses, and squares based on the properties of their side lengths and angles.
• Identify and draw lines of symmetry in two-dimensional figures.
• Solve problems involving unknown side lengths, perimeter, area, and angle measurements using the known attributes and properties of two-dimensional shapes.

It is directly aligned to 4th Grade IM Unit 8 Section B. This is only for ALL Unit 8 Lessons 1-10. There are one/two sheets per lesson. There is no page for Lesson 10 since it is an optional lesson.

• Lesson 1: Ways to Look at Figures
• Lesson 2: Ways to Look at Triangles
• Lesson 3: Ways to Look at Quadrilaterals
• Lesson 4: Symmetry in Figures (Part 1)
• Lesson 5: Symmetry in Figures (Part 2)
• Lesson 6: All Kinds of Attributes (Optional Lesson) *included*
• Lesson 7: Ways to Find Unknown Lengths (Part 1)
• Lesson 8: Ways to Find Unknown Lengths (Part 2)
• Lesson 9: Symmetry in Action (Optional Lesson) *included*
• Lesson 10: Ways to Find Angle Measurements (Optional Lesson) not included

Click here for Illustrative Math: 4th Grade Unit 8 - Choice Board/Centers

Click here for Illustrative Math: 4th Grade Unit 8 - Section A

Click here for Illustrative Math: 4th Grade Unit 8 - Section B

Click here for Illustrative Math: 4th Grade Unit 8 - Full Unit

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