Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
Purpose and Instructional Strategies
- The purpose of this benchmark is to give students authentic opportunities to estimate multiplication and division. This work builds on students rounding to the nearest 10 or 100 without performing operations (MA.3.NSO.1.4).
- When students find exact solutions of multiplication and division problems, they should use mental math and computation strategies to estimate to determine if their solution is reasonable (MTR.6.1).
- Estimation is often about getting useful answers that need not be exact.
- Students should be able to explain their reasoning.
Common Misconceptions or Errors
- Some students may not understand how an approximate answer can be useful.
- Students may obsess over whether they got the same estimate as someone else. This can
be resolved when the teacher explains that both estimates are useful and acceptable.
Strategies to Support Tiered Instruction
- Instruction includes relating estimation strategies to real-world situations.
- For example, an art teacher has 10 classes with the following numbers of
students, 21, 25, 18, 27, 23, 27, 30, 28, 30, 26. He wants to buy 12 pencils for each student. Discuss with students why a suitable estimate could be 12×10×30.
Instructional Task 1 (MTR.7.1)
Mrs. Diaz bought 50 packages of crayons to give to her art class. Each package contains 8 individual crayons. She wants to give an equal number of crayons to each of the 22 students in the class.
- Part A. One student estimated that each student in Mrs. Diaz’ class would get 10 crayons. Do you think this is a good estimate? Why or why not?
- Part B. Use estimation to determine about how many crayons each student will get. Write your answer below and explain your reasoning.
Instructional Item 1
Marianela bought 33 packages of pink erasers and 25 packages of glow-in-the-dark erasers for the school store. Packages of pink erasers cost $12 each and packages of glow-in-the-dark erasers cost $19 each. Marianela says she spent about $850, is her answer reasonable? Explain.
- a. Yes, because (30 × $10) + (25 × $20) = $800.
- b. Yes, because (30 × 25) + ($10 × $20) = $950.
- c. No, because (30 × 30) + ($10 × $20) = $1,100.
- d. No, because (30 + 30) × ($10 × $20) = $1,200.
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.