Illustrative Mathematics
Reasoning about Multiplication and Division and Place Value, Part 1
Help your class make sense of quantities and their relationships. Given is the product of two numbers. It is up to your number crunchers to think about the quantitative relationship when the product is one-tenth or ten times the product...
Illustrative Mathematics
Find the Angle
This a fun problem for young geometers to play with while gaining important insight into deductive reasoning. Some will find the answers very quickly, others might take a less direct path, but all will use their knowledge of the sum of...
Illustrative Mathematics
Reasoning about Multiplication
In critiquing someone else's theory, learners share insight into their own understanding of mathematical concepts. Fifth graders will explore the notion that products are always larger than their factors. While this statement is...
CCSS Math Activities
Smarter Balanced Sample Items: 7th Grade Math – Claim 3
Does the explanation make sense? Sample items highlight claim three, communicating reason, in the Smarter Balanced assessments. Teachers use the 16 items to help show pupils the importance of communication and reasoning within...
Curated OER
How does the solution change?
Four simple equations, each with two variables, try to get at the important question of reasoning about equations. The problem isn't to solve the equations, but to understand the nature of their solutions. These equations address the...
Noyce Foundation
Photographs
Scaling needs to be picture perfect. Pupils use proportional reasoning to find the missing dimension of a photo. Class members determine the sizes of paper needed for two configurations of pictures in the short assessment task.
EngageNY
Mid-Module Assessment Task: Grade 7 Mathematics Module 4
Assess the ability of the class to solve percent problems with an assessment that covers a variety of percent problems from basic to multi-step. Pupils make connections between percent problems and proportional thinking to complete...
EngageNY
Tax, Commissions, Fees, and Other Real-World Percent Problems
Pupils work several real-world problems that use percents in the 11th portion of a 20-part series. The problems contain percents involved with taxes, commissions, discounts, tips, fees, and interest. Scholars use the equations formed for...
Noyce Foundation
Boxes
Teach your class to think outside the box. Scholars use the concept of equality to solve a problem in the assessment task. They determine how to use a scale to identify the one box out of a set of nine boxes that is heavier than the others.
Curated OER
Rounding and Subtracting
Common Core is all about getting your learners to open their minds and think about the why and how. This problem has them thinking about unknown numbers and their relationship with one another when we round and...
Curated OER
College Athletes
When more basketball players are taller than field hockey players at a school, is it safe to say that in general they are always taller? The activity takes data from two college teams and your learners will be able to answer questions...
Illustrative Mathematics
Walk-a-thon 1
Your mathematician's job is to explore the relationship between hours and miles walked during a walk-a-thon. The activity compels your learners to experiment with different means in finding out this proportional relationship. The answer...
EngageNY
Mid-Module Assessment Task - Algebra 1 (module 4)
Performance task questions are the most difficult to write. Use this assessment so you don't have to! These questions assess factoring quadratics, modeling with quadratics, and key features of quadratic graphs. All questions require...
Illustrative Mathematics
How Many Containers in One Cup / Cups in One Container?
The object is to model fraction division by asking “How many are in one group?” It is a difficult concept to understand, but developing the model that shows one cup to a certain amount of container or one container to a certain amount of...
Illustrative Mathematics
Jim and Jesse's Money
Jim and Jesse started their road trip with the same amount of money. Your class must find the amount of money each one had given, the amount of money spent, and the ratio of money at the end. This is a comprehensive problem that...
Illustrative Mathematics
Voting for Three, Variation 3
Get your learners to think outside the box. Students require a good understanding of ratios and their relationship to fractions to complete the problem. The only quantities given in the problem are the ratio of the number of votes for...
Curated OER
Why Does ASA Work?
Your geometry learners explore Angle-Side-Angle congruence in this collaborative task. The sum of the interior angles of all triangles being one hundred eighty degrees, is the key learners will discover as they explain their reasoning...
Balanced Assessment
Fractured Subtraction
Can you spare a 10? Scholars determine digits that could complete a two-digit subtraction problem. They must find all possible combinations of digits and provide an explanation for their reasoning.
EngageNY
End-of-Module Assessment Task - Grade 8 Mathematics (Module 2)
Can your classes apply the knowledge they have learned? Use this performance task to find out! Individuals use transformations to explain congruence and angle relationships within parallel lines to find missing values. They show what...
Mathed Up!
Shading Fractions of Rectangles
Learners find the midpoint between two numbers, shade fractional amounts of rectangles as well as decimal amounts of rectangles, and explain their mathematical reasoning in words. The assessment is a great way to check for understanding...
College Board
2003 AP® Environmental Science Free-Response Questions
One size fits all doesn't seem to be the right approach to endangered species. Using a four-part AP® assessment, learners respond to questions that address environmental concerns such as human population changes, invasive species...
College Board
2011 AP® English Language and Composition Free-Response Questions Form B
Strong writers support their points with direct evidence and details. A series of free-response questions from the 2011 AP® English Language and Composition exam require the use of details to obtain a good score. The first prompt...
Illustrative Mathematics
Converting Square Units
Jada has a rectangle board that is measured in inches. Young learners confirm their understanding of converting inches to feet. Then they find the area in square feet. Jada thinks she has a short-cut to convert inches square to square...
EngageNY
Ratios of Fractions and Their Unit Rates 2
Remodeling projects require more than just a good design — they involve complex fractions, too. To determine whether a tiling project will fit within a given budget pupils calculate the square footage to determine the number of...