# MA.4.NSO.2.5

Explore the multiplication and division of multi-digit whole numbers using estimation, rounding and place value.

### 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.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Number Sense and Operations
Status: State Board Approved

## Benchmark Instructional Guide

• 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.

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

This benchmark is part of these courses.
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712050: Access Mathematics Grade 4 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.4.NSO.2.AP.5: Explore the estimation of products and quotients of two whole numbers up to two digits by one digit.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessment

Estimating the Solution:

Students are asked to use a mental estimation strategy to evaluate the solution of a multistep word problem.

Type: Formative Assessment

## Lesson Plans

Order_in_the_School_Zone_Part_3:

Students will work in pairs or small groups. They will be provided with a “school district” and zones. The groups will be tasked with assigning each zone to a school, while respecting the school's enrollment caps and the zone's proximity to the school.  Once the zones are assigned, the students will calculate the approximate busing costs.  Then, the groups will pair off and compare how they determined zoning for each school.

Type: Lesson Plan

I See! Division with the Distributive Property:

In this lesson, students will use visual models to represent division using the distributive property as a strategy. Students will have an understanding of how to decompose numbers in the context of division problems using an area model.

Type: Lesson Plan

Lizard Lights:

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.

Type: Lesson Plan

## Perspectives Video: Expert

B.E.S.T. Journey:

What roles do exploration, procedural reliability, automaticity, and procedural fluency play in a student's journey through the B.E.S.T. benchmarks? Dr. Lawrence Gray explains the path through the B.E.S.T. mathematics benchmarks in this Expert Perspectives video.

Type: Perspectives Video: Expert

## Perspectives Video: Teaching Ideas

Multiplying Multi-digit Numbers:

Unlock an effective teaching strategy for teaching multiplying multi-digit numbers using ten frames in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Estimating Decimal Multiplication:

Unlock an effective teaching strategy for teaching decimal multiplication in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

## STEM Lessons - Model Eliciting Activity

Lizard Lights:

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.

## MFAS Formative Assessments

Estimating the Solution:

Students are asked to use a mental estimation strategy to evaluate the solution of a multistep word problem.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.