### Examples

*Example:*The product of 6 and 70 is 420.

*Example:* The product of 6 and 300 is 1,800.

### Clarifications

*Clarification 1:*When multiplying one-digit numbers by multiples of 10 or 100, instruction focuses on methods that are based on place value.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**3

**Strand:**Number Sense and Operations

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- Expression
- Equation
- Factor
- Whole Number

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

The purpose of this benchmark is for students to use place value reasoning to multiply single- digit factors (0-9) by multiples of 10 up to 90 (10, 20, 30, 40, 50, 60, 70, 80, 90) and multiples of 100 up to 900 (100, 200, 300, 400, 500, 600, 700, 800, 900). Because the expectation of this benchmark is at the procedural reliability level, students should develop accurate, reliable methods for multiplication that align with their understanding and learning style.- Instruction should connect known facts of one-digit factors (e.g., 6 × 7), to then apply to products of one-digit numbers and multiples of 10 or 100 (e.g., 6 × 70, 60 × 7, 6 ×
700, 600 × 7)
*(MTR.5.1).* - Teachers should use place value representations (e.g., pictures, diagrams, base ten blocks,
place value chips) to show relationships between known facts and multiplying one-digit factors by multiples of 10 or 100. For example, 3 × 4 can be interpreted as 3 groups of 4 ones, or 12 ones. 3 × 40 can be represented as 3 groups of 4 tens, or 12 tens. 12 tens is equal to 120 ones. 3 × 400 can be represented as 3 groups of 4 hundreds, or 12 hundreds. 12 hundreds is equal to 120 tens or 1,200 ones
*(MTR.5.1).* - This standard lays the foundation for multi-digit multiplication. For benchmark 3.AR.1.1, students use the distributive property to multiply 34 × 8 as (30 × 8) + (4 × 8). This benchmark (MA.3.NSO.2.3) helps students reason that 30 $x$ 8 is the same as 3
*tens*× 8, or 24*tens*(240). - Instruction should not focus on “adding zeroes to the end” when multiplying one-digit factors by multiples of 10 and 100. For example, 7 $x$ 50 should not be reduced to “7 × 5 with one zero at the end.” This trick does not focus on place value methods, as Clarification #1 of the benchmark requires.

### Common Misconceptions or Errors

- Students can quickly jump to the conclusion that they can “count zeroes” to determine the number of zeroes in the product (e.g., the product of 7 $x$ 500 will have two zeroes because 500 has two zeroes). This can confuse students when the products of the known facts already end in zero (e.g., using 5 × 8 = 40 to multiply 5 × 80). Students who rely on this trick will often indicate that 5 × 80 = 40 because they see only one zero in the factors.

### Strategies to Support Tiered Instruction

- Instruction includes opportunities to connect grouping numbers by multiples in different ways.
- For example, students may place the following facts on the hundreds chart: 1 × 10, 2 × 10, 3 × 10, 4 × 10, 5 × 10, 6 × 10, 7 × 10, 8 × 10 and 9 × 10. The teacher asks students what patterns they notice.

- Instruction includes opportunities to use a number line. Students skip count by multiples on the number line. This will support a conceptual understanding of what is happening with the numbers, instead of focusing on the “zero trick.” 2×200 = 400

- Instruction includes opportunities to connect grouping numbers by multiples.
- For example, students use manipulatives to show that 5 groups of 20 is 100 and 5 groups of 200 is 1,000. Teacher should be explicit about the multiples and not point out the zeros trick.

### Instructional Tasks

*Instructional Task 1*

- The table below shows the costs for entry at the Sunnyland Amusement Park.

- a. How much does entry cost for nine adults? Write an equation to show the total cost?
- b. Write an expression that shows the total cost for one senior and one 2-year-old child to attend Sunnyland Amusement Park.
- c. The Suarez Family purchases 2 adult tickets, 1 senior ticket, and 1 ticket for their 6- year-old daughter. Write an equation to show the total cost of entry for the family.
- d. Which cost of entry is less expensive, 2 seniors or 3 children? Explain how you know using words, a picture, or equations.

### Instructional Items

*Instructional Item 1 *

- Write two different equations using a one-digit whole number and a multiple of 10 that show a product of 120.

*Instructional Item 2 *

- Write two different equations using a one-digit whole number and a multiple of 100 that show a product of 2,400.

**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 Assessments

## Lesson Plans

## Original Student Tutorials

## Perspectives Video: Experts

## Perspectives Video: Teaching Idea

## STEM Lessons - Model Eliciting Activity

In this Model Eliciting Activity, MEA, students will choose their top choices of field day activities given the area required for event, safety concerns, clean up required, number of students that can play at a time, and peer comments about the activity. Students will need to make trade-offs in cost when the "twist" provides budget restrictions. Students will count unit squares to calculate area, multiply one-digit numbers by multiples of ten, and add multi-digit whole numbers.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

In this Model Eliciting Activity, MEA, students will be required to rank musical instrument lesson packages based on the price, the number of minutes of practice each week, and the quality of the instructor.

Part of the task involves students figuring out the elapsed time of the lessons based on their start and stop times. They will also need to figure out the total weekly cost of the lessons based on the number of lessons offered per week and the cost of each lesson based on its length.

The twist will require students to determine whether or not to revise their ranking based on new information about the cost of instrument rentals per lesson and the class size of each package.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Batter Up!!! Help the Peace Love Baseball Championship find a home!!! In this interactive Model-Eliciting Activity (MEA), the students will successfully multiply one digit whole numbers by multiples of 10. The students will also work collaboratively to express their opinions, while considering those of their peers.

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.

In this MEA, students will work in groups to rank books using the following criteria: price, genre, number of pages, reading level and a summary provided for each book. The students must calculate the price for a class set of each book by multiplying each price by 20 students. There is a budget of $100. Students are then given a new budget and a new criteria and asked to re-evaluate their decision.

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.

In this model-eliciting activity (MEA), students will work together to determine the best bus for a class trip. Students will be able to decide between several buses with varying capabilities and costs while practicing their application of multiplying one-digit whole numbers by a multiple of ten.

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.

In this Model Eliciting Activity, MEA, students will help the Sweet Donut Shop determine what the newest donut will be. Students are given the cost to make each batch along with the selling price and are asked to determine the profit for each batch. Students create a procedure for ranking the donuts and write a letter explaining the procedure and the ranking. In the “twist” students are provided the starting and finishing times for each batch. They must determine the total amount of time, decide if their procedure should change based on the new information, and write a letter explaining whether the procedure changed and the new ranking of the donuts.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

In this Model Eliciting Activity, MEA, students will determine which mode of transportation is best for a traveling sports team. They will have to calculate the total cost for each type of transportation and consider the comfort of travel. In the "twist," students are provided with more information including customer service rating of transportation as well as an additional choice. Students must also calculate the arrival time when given the departure time and the elapsed time to determine if the team will be arriving in time. Additionally, students learn about an option to have a chance to win a drawing based on the cost of the transportation option selected.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

In this Model Eliciting Activity, MEA, The Shady Oak Treehouse Club is doing a makeover and needs help choosing flooring. Students will be asked to figure area, calculate cost, and add installation fees to cost. The students will then rank the flooring and choose the best one for the makeover. The data provided is: a model of the treehouse (in square yards), flooring price per square yard, and ratings for ease of cleaning, comfort, and color choices. In the twist, student will be provided with an installation fee for each flooring material and must decide if, and how, to change their procedure with the new information.

## MFAS Formative Assessments

Students are asked to explain why, when multiplying by a power of 10, the product has a zero in the ones place.

Students are asked to consider how using an easier, known fact could help them solve a related multiplication problem with a multiple of 10.

Students are asked to explain how the knowing the product of nine and three can help in finding the product of nine and 30.

Students consider the solution to a multiplication problem and explain their thinking.

## Original Student Tutorials Mathematics - Grades K-5

Learn how to multiply a 1-digit number by ten using a pattern to help you. This interactive tutorial is Part 1 in a two-part series about multiplying by multiples of ten.

Learn to multiply by multiples of ten, in this interactive tutorial!

This is the second tutorial in a two-part series. .

## Student Resources

## Original Student Tutorials

Learn to multiply by multiples of ten, in this interactive tutorial!

This is the second tutorial in a two-part series. .

Type: Original Student Tutorial

Learn how to multiply a 1-digit number by ten using a pattern to help you. This interactive tutorial is Part 1 in a two-part series about multiplying by multiples of ten.

Type: Original Student Tutorial