Illustrative Mathematics
Illustrative Mathematics: Running to School
This is the easiest problem in a series of three tasks involving fraction multiplication that can be solved with pictures or number lines. Aligns with 5.NF.B.6.
Illustrative Mathematics
Illustrative Mathematics: Finding Common Denominators to Add
Part (a) of this task asks young scholars to find and use two different common denominators to add the given fractions. The purpose of this question is to help students realize that they can use any common denominator to find a solution,...
Illustrative Mathematics
Illustrative Mathematics: 6.ee Busy Day
This problem can be solved using simple arithmetical reasoning but is also naturally represented by a simple equation. Thus, it provides a good entry point for students into representing quantities in contexts with variables and...
Illustrative Mathematics
Illustrative Mathematics: 4.oa Comparing Money Raised
The purpose of this task is for students to solve three comparisons problems that are related by their context but are structurally different. Multiplicative comparison is purposefully excluded from third grade (see 3.OA.3 and 3.MD.2),...
Illustrative Mathematics
Illustrative Mathematics: S Id.4 Do You Fit in This Car?
Students are tasked with solving a common issue for automobile manufacturers that require the students to use normal distribution as a model for data distribution. They will also use mean and standard deviation to figure out the problem....
Illustrative Mathematics
Illustrative Mathematics: S Id, F if Laptop Battery Charge
This task uses a situation that is familiar to students to solve a problem they probably have all encountered before: How long will it take until an electronic device has a fully charged battery? Given data, students perform a variety of...
Illustrative Mathematics
Illustrative Mathematics: G C, G Srt Setting Up Sprinklers
In this task, students must decide where to place sprinklers on a lawn so that the maximum area of the lawn will be watered. To solve it, they must find areas of sectors of circles and use trigonometric ratios to solve right triangles....
Illustrative Mathematics
Illustrative Mathematics: 6.rp Voting for Two, Variation 4
Students use ratio reasoning to solve the following performance task: John and Will ran for 6th grade class president. John got two votes for every vote Will got. It was necessary to get more than half the votes to get elected. What...
Illustrative Mathematics
Illustrative Mathematics: 6.rp Voting for Two, Variation 3
Students use ratios to solve the following performance task: John and Will ran for 6th grade class president. There were 36 students voting. John got two votes for every vote Will got. It was necessary to get more than half the votes to...
Illustrative Mathematics
Illustrative Mathematics: 6.rp Voting for Two, Variation 2
Students use ratios to solve the following performance task: John and Will ran for 6th grade class president. There were 36 students voting. John got two votes for every vote Will got. How many more votes did John get than Will?
Illustrative Mathematics
Illustrative Mathematics: 6.rp Shirt Sale
Students use ratio and rate reasoning to solve the following performance task: Selina bought a shirt on sale that was 20% less than the original price. The original price was $5 more than the sale price. What was the original price?...
Illustrative Mathematics
Illustrative Mathematics: Building Toward Fluency
The purpose of this task is to promote certain addition strategies that will help students learn to fluently add and subtract within 20. Students will use a number line or magnetic cubes to solve addition problems. Students will be asked...
Illustrative Mathematics
Illustrative Mathematics: 6.rp Dana's House
Students use ratio and rate to solve this real-world math performance task: The lot that Dana is buying for her new one story house is 35 yards by 50 yards. Dana's house plans show that her house will cover 1,600 square feet of land....
Illustrative Mathematics
Illustrative Mathematics: A Rei Pairs of Whole Numbers
The premise of this problem is simple - students must find three whole numbers with three different sums when they are added in pairs. To do this, they set up a system of linear equations in three variables. Aligns with A-REI.C.6.
Illustrative Mathematics
Illustrative Mathematics: G Srt, G Mg How Far Is the Horizon?
Some friends are at the beach looking out onto the ocean on a clear day and they wonder how far away the horizon is. A second problem asks how far the horizon would be from the top of a mountain. Students must also answer a question...
Illustrative Mathematics
Illustrative Mathematics: G Gmd Centerpiece
This problem presents a wedding reception scenario. The bride is creating centerpieces for the tables and must calculate how many marbles she needs to partly fill the vases and stay within her budget at the same time. Aligns with G-GMD.A.3.