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

**Grade:**4

**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

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

- The purpose of this benchmark is for students to become procedurally fluent in using a standard algorithm. Work with standard algorithms began in the procedural reliability stage when students explored a variety of methods and learned to use at least one of those methods accurately and reliably.
- It is important to challenge students to explain the steps they follow when using a standard algorithm (i.e. regrouping, proper recording, and placement of digits by place value).

### Common Misconceptions or Errors

- Students that are taught a standard algorithm without any conceptual understanding will often make mistakes. For students to understand a standard algorithm or any other method, they need to be able to explain the process of the method they chose and why it works. This explanation may include pictures, properties of multiplication, decomposition, etc.
- Some students may struggle with this benchmark if they do not have a strong command of basic addition and multiplication facts.

### Strategies to Support Tiered Instruction

- Instruction includes explaining mathematical reasoning while using a multiplication algorithm. Instruction also includes determining if an algorithm was used correctly by reviewing the reasonableness of solutions.
- For example, students use an algorithm to determine 41 × 23 and explain their thinking using place value understanding. Explicit instruction includes: “Begin by multiplying 3
*ones*times 1*one*. This equals 3*ones*. We will write the 3*ones*under the line, in the ones place. Next, we will multiply 3*ones*times 4*tens*. This equals 12*tens*. We will write the 12*tens*under the line in the hundreds and tens place because 12*tens*is the same as 1*hundred*and 2*tens*. This gives us our first partial product of 123. Now we will multiply the 1*one*by the 2*tens*from 23. This equals 2*tens*or 20. We will record 20 below our first partial product of 123. Next, we, we will multiply 2*tens*times 4*tens*, which equals 8*hundreds*. We will write the 8 in the hundreds place of our second partial product. Our second partial product is 820. Finally, we add our partial products to find the product of 943.”

- For example, students use an algorithm to determine 41 × 23 and explain their thinking using place value understanding. Explicit instruction includes: “Begin by multiplying 3

- For example, students determine 41 × 23 using an area model and place value understanding.

- For example, students use an algorithm to determine 4 × 36 and explain their thinking using place value understanding. Instruction includes stating, “Begin by multiplying 4
*ones*times 6*ones*. This equals 24*ones*or 2*tens*and 4*ones*. We will write the 4*ones*from 24 under the line, in the one's place. We will write the 2*tens*from 24 as a 2 above the 3, as a regrouped digit in the tens place. Next, we will multiply 4*ones*times 3*tens*. This equals 12*tens*. We will add the 2*tens*to the 12*tens*for a total of 14*tens*. We will write the 14*tens*under the line in the hundreds and tens place because 14*tens*is the same as 1*hundred*and 4*tens*. Our product is 144.”

- For example, students determine 4 × 36 using an area model and place value understanding.

- Instruction includes the use of known facts to find unknown multiplication facts.
- For example, if the student does not know the product for 4 × 6 from the previous 120 +24 144 example, have students use a known fact such as 4 × 5. The known fact of 4 × 5 = 20 can be used to find the product of 4 × 6 by adding one more group of 4 to the product of 20 to find the product of 24.

### Instructional Tasks

*Instructional Task 1* (MTR.4.1, MTR.5.1)

### Instructional Items

*Instructional Item 1*

- a. 10×48
- b. 16×30
- c. 24×24
- d. 32×15
- e. 40×80

**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: Experts

## Perspectives Video: Teaching Idea

## Tutorials

## STEM Lessons - Model Eliciting Activity

In this Model Eliciting Activity, MEA, students will help a party planner determine which party location is the best one to use. They will calculate the cost of the banquet hall rental based on the number of people, number of tables and hourly rental of the location by using division and multiplication.

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 decide which type of protective surface should be put in under a new playground unit. They will consider many factors before ranking their decisions about the best surface.

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

Students are asked to multiply a pair of two-digit numbers using a strategy based on place value.

## Student Resources

## Tutorials

In this video tutorial from Khan Academy, view a demonstration of how to set-up an area model for multiplying a two-digit number by a two-digit number on graph or grid paper and then link this to the standard algorithm.

Type: Tutorial

In this tutorial video from Khan Academy, view an example of how to multiply a two-digit number by a two-digit number using the area model. The video makes a connection between partial products and the area model.

Type: Tutorial

In this tutorial video from Khan Academy, view an example of how to multiply a 2-digit number by another 2-digit number. Be sure to stick around for the second example! The key is understanding the value of each digit!

Type: Tutorial

In this video tutorial from Khan Academy, view an example of how to solve a problem in which a **3-digit** number is being multiplied by a 1-digit number using the standard algorithm.

Type: Tutorial

In this video tutorial from Khan Academy, view an example of how to solve a multiplication problem with a two-digit number multiplied by a one-digit number using the standard algorithm.

Type: Tutorial

## Parent Resources

## Tutorials

In this video tutorial from Khan Academy, view a demonstration of how to set-up an area model for multiplying a two-digit number by a two-digit number on graph or grid paper and then link this to the standard algorithm.

Type: Tutorial

In this tutorial video from Khan Academy, view an example of how to multiply a two-digit number by a two-digit number using the area model. The video makes a connection between partial products and the area model.

Type: Tutorial

In this tutorial video from Khan Academy, view an example of how to multiply a 2-digit number by another 2-digit number. Be sure to stick around for the second example! The key is understanding the value of each digit!

Type: Tutorial

In this video tutorial from Khan Academy, view an example of how to solve a problem in which a **3-digit** number is being multiplied by a 1-digit number using the standard algorithm.

Type: Tutorial

In this video tutorial from Khan Academy, view an example of how to solve a multiplication problem with a two-digit number multiplied by a one-digit number using the standard algorithm.

Type: Tutorial