Illustrative Mathematics
Illustrative Mathematics: 6.rp, 6.ee Fruit Salad
A fruit salad consists of blueberries, raspberries, grapes, and cherries. The fruit salad has a total of 280 pieces of fruit. There are twice as many raspberries as blueberries, three times as many grapes as cherries, and four times as...
Illustrative Mathematics
Illustrative Mathematics: 6.rp Voting for Three, Variation 3
Students use simple ratios to answer the following question: John, Marie, and Will all ran for 6th grade class president. The ratio of votes for John to votes for Will was two to one. Marie got exactly the average number of votes for the...
Illustrative Mathematics
Illustrative Mathematics: 6.rp Voting for Three, Variation 2
John, Marie, and Will all ran for 6th grade class president. Of the 36 learners voting, the ratio of votes for John to votes for Will was two to one. Marie got exactly the average number of votes for the three of them. How many more...
Illustrative Mathematics
Illustrative Mathematics: 6.rp Voting for Three, Variation 1
Students use ratio relationships between two quantities to answer three questions in this diagram-based performance task.
Illustrative Mathematics
Illustrative Mathematics: 6.rp Running at a Constant Speed
Learners use ratio and rate reasoning to answer four questions in this performance task.
Illustrative Mathematics
Illustrative Mathematics: 6.rp Security Camera
Students use ratio and rate reasoning to answer four questions in this diagram-based performance task.
Illustrative Mathematics
Illustrative Mathematics: 6.rp Friends Meeting on Bicycles
Students use ratio and rate to answer five questions in this real-world math performance task.
Illustrative Mathematics
Illustrative Mathematics: 6.rp Kendall's Vase Tax
Students use percentage and addition to answer this real-world math performance task: Kendall bought a vase that was priced at $450. In addition, she had to pay 3% sales tax. How much did she pay for the vase?
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: 6.rp Mixing Concrete
Students use ratio and rate to answer this performance task: A mixture of concrete is made up of sand and cement in a ratio of 5 : 3. How many cubic feet of each are needed to make 160 cubic feet of concrete mix?
Illustrative Mathematics
Illustrative Mathematics: 6.rp Currency Exchange
Students use ratio and rate to answer this performance task: Joe was planning a business trip to Canada, so he went to the bank to exchange $200 U.S. dollars for Canadian dollars (at a rate of $1.02 CDN per $1 US). On the way home from...
Illustrative Mathematics
Illustrative Mathematics: 6.rp Converting Square Units
In this task, 6th graders must inches to feet in order to find the area of a rectangular board and explain the error in the calculations made by the board owner. Aligns with 6.RP.A.3.
Illustrative Mathematics
Illustrative Mathematics: 6.rp Jim and Jesse's Money
In this real-world context, 6th graders are given the ratio of Jim's money to Jesse's and the amounts they have spent so far on a road trip, and they must calculate what each person had at the start of the trip. Aligns with 6.RP.A.3.
Illustrative Mathematics
Illustrative Mathematics: 6.g Painting a Barn
This task asks students to determine the area of the exterior walls of a barn and to calculate how many gallons of paint would be needed to cover them, as well as the cost of the paint. Aligns with 6.G.A and 6.RP.A.3.
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Better Lesson: Finals Week Day 2
Which drink has the strongest caffeine concentration? Students work on this problem for the second of two lessons.
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Better Lesson: Understanding Tape Diagrams
Using a tape diagram is one of the key models for ratios and proportions.
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Better Lesson: The Double Number Line
The double number line will help students figure out problems that involve two quantities.
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Better Lesson: Using a Ratio Table
The ratio table is a tool that students can use to solve a variety of problems.
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Better Lesson: The Chances Are, You Will Do Great! A Review of Probability
An engaging review that not only allows students to practice their skills but also maintains a slight edge of competitiveness!
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Better Lesson: Loans and Savings
What are loans and how do they work? How do banks encourage people to save money? Students work on these questions in the context of the College Project.
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Better Lesson: Nana's Chocolate Milk
How can you fix Nana's chocolate milk? Students work on this problem over time to develop a final product that demonstrates their mathematical thinking and solution.
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Better Lesson: Finals Week Day 1
Sixth graders define rate and give examples of how they can use rates.