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Examples
Example: The product of 215 and 460 can be estimated as being between 80,000 and 125,000 because it is bigger than 200×400 but smaller than 250×500.Example: The quotient of 1,380 and 27 can be estimated as 50 because 27 is close to 30 and 1,380 is close to 1,500. 1,500 divided by 30 is the same as 150 tens divided by 3 tens which is 5 tens, or 50.
Clarifications
Clarification 1: Instruction focuses on previous understanding of multiplication with multiples of 10 and 100, and seeing division as a missing factor problem.Clarification 2: Estimating quotients builds the foundation for division using a standard algorithm.
Clarification 3: When estimating the division of whole numbers, dividends are limited to up to four digits and divisors are limited to up to two digits.
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Expression
- Equation
- Factor
Vertical Alignment
Previous Benchmarks
Next Benchmarks
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 Tasks
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 Items
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.
Related Courses
Related Access Points
Related Resources
Formative Assessment
Lesson Plans
Perspectives Video: Expert
Perspectives Video: Teaching Ideas
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Students will use a real-world problem solving situation to determine the best types of light bulbs to maintain an appropriate environment for a captive lizard.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
MFAS Formative Assessments
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