Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Equal Sign
- Number Line
Purpose and Instructional Strategies
In grade 5, students multiplied and divided decimals by one tenth and one hundredth, added and subtracted fractions with unlike denominators, and determined if equations were true. In grade 6, students increase their computation with fractions and decimals as well as solve equations with integers. In grade 7, students solve multi-step equations with rational numbers.
- Thinking through the lens of fact families can help students think flexibly about number relationships to determine the unknown value (MTR.5.1).
- This benchmark allows for fractions in equations to include unlike denominators.
- The benchmark expects students to reason and use mental math to build their number sense. Students should not follow a specific set of steps to solve.
- Variables are not limited to ; instruction includes using a variety of lowercase letters for their variables; however, , and should be avoided as they too closely resemble zero and one.
Common Misconceptions or Errors
- Students may not see the connection to mental mathematics within the benchmark and instead try to apply rules and procedures when finding an unknown quantity.
Strategies to Support Tiered Instruction
- Instruction includes the use of fact family prompts of whole numbers to help guide students reasoning with positive rational numbers.
- For example, the connection can be made between determining the unknown in the equation 3 × = 15 and in the equation × = .
- Teacher provides opportunities for students to identify the relationship between the provided numbers and then co-solve the equation to determine the unknown.
Instructional Task 1 (MTR.4.1)
- Given the equation 0.5 = , describe a process or create a visual to explain how you can determine the value of c.
Instructional Task 2 (MTR.4.1)
- If 29 + g = 89, what value of g makes the equation true? Support your response with evidence.
Instructional Task 3 (MTR.7.1)
- A solar panel can generate 825 of a kilowatt of power. The average store needs to generate about 30 kilowatts of power.
- Part A. Write an equation to determine how many solar panels a store needs on its roof.
- Part B. How many solar panels does a store need?
Instructional Item 1
- Determine the value of m in the equation 0.15m = 0.60.
Instructional Item 2
- Given the equation p −35 = 710, what value of p could be a solution to the equation?
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.