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

**Grade:**7

**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

- Rational Number

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 6, students performed operations with integers, multiplied and divided positive multi-digit numbers with decimals to the thousandths and computed products and quotients of positive fractions by positive fractions, including mixed numbers with procedural fluency. In grade 7, students perform all four operations with positive and negative rational numbers with procedural fluency. In grade 8, they will expand to operations with rational numbers including exponents and radicals, and will perform operations with rational numbers expressed in scientific notation.- This benchmark is the completion of arithmetic operations with rational numbers
*(MTR.3.1).* - Instruction includes the possibility that the division of two fractions can be written as a complex fraction. This connection will be important when students work with algebraic expressions in later grades.
- Students should develop fluency with and without the use of a calculator when performing operations with rational numbers.

### Common Misconceptions or Errors

- Students may think the product of a fraction and another fraction is greater than either factor. Use manipulatives or models referenced in previous grade levels to support conceptual understanding
*(MTR.2.1).* - Students may incorrectly believe that dividing by $\frac{\text{1}}{\text{2}}$ is the same as dividing by 2.
- Students may incorrectly solve complex fractions by multiplying the two fractions.

### Strategies to Support Tiered Instruction

- Instruction includes the use of fraction tiles to represent operations with positive fractions while simultaneously recording the equivalent numerical expressions.
- Instruction includes the use of base ten blocks to represent operations with positive decimals while simultaneously recording the equivalent numerical expressions.
- Instruction includes the use of two-color counters to represent operations with positive and negative whole numbers while simultaneously recording the equivalent numerical expressions.
- Teacher co-creates a graphic organizer with students to review operations with positive fractions and operations with integers to assist when applying operations with rational numbers.
- Instruction includes using manipulatives or models referenced in previous grade levels to support conceptual understanding.

### Instructional Tasks

*Instructional Task 1*

**(MTR.7.1)**Daliah purchases eggs by the dozen for her two children. Each day, Zane eats $\frac{\text{1}}{\text{4}}$ carton and Amare eats $\frac{\text{1}}{\text{6}}$ carton. A carton of 12 eggs costs $1.65.

- Part A. How much does Daliah spend on eggs for her two children in 30 days?
- Part B. During one of her shopping trips, Daliah finds that her grocery store has started to sell cartons of 18 eggs for $2.25. If she begins to purchase these cartons, how much does Daliah spend on eggs for her two children in 30 days? After how many days will Daliah spend more than $50? Explain your reasoning.

Instructional Task 2

Instructional Task 2

**(MTR.3.1)**Given $a$ = −2$\frac{\text{3}}{\text{5}}$ and $b$ = $\frac{\text{2}}{\text{3}}$, calculate the following:

- $a$ + $b$
- $a$ − $b$
- $a$ · $b$
- $\frac{\text{a}}{\text{b}}$

### Instructional Items

*Instructional Item 1*

Determine the product of $\frac{\text{15}}{\text{6}}$ and −1.2.

*Instructional Item 2*

What is the value of the expression 7.24 − 5.01 − 78.4?

*Instructional Item 3*

What is the value of the expression

**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

## Educational Game

## Educational Software / Tool

## Formative Assessments

## Lesson Plans

## Perspectives Video: Experts

## Problem-Solving Task

## Tutorial

## Video/Audio/Animation

## STEM Lessons - Model Eliciting Activity

In this Model Eliciting Activity, MEA, students will research a list of companies to invest in through purchasing stocks. Students will calculate the amount invested and readjust their investment choices.

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 add, subtract, multiply, and divide positive and negative fractions.

Students are asked to evaluate expressions involving multiplication of rational numbers and use the properties of operations to simplify calculations.

Students are asked to rewrite complex fractions as simple fractions in lowest terms.

Students are asked to describe a real-world context for a given expression involving the product of two rational numbers.

Students are asked to combine rational numbers, including fractions and decimals, and use the properties of operations to simplify calculations.

Students are asked to explain why the product of a positive and a negative rational number is negative.

## Student Resources

## Educational Game

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Type: Educational Game

## Educational Software / Tool

In this activity, students solve arithmetic problems involving whole numbers, integers, addition, subtraction, multiplication, and division. This activity allows students to track their progress in learning how to perform arithmetic on whole numbers and integers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Software / Tool

## Problem-Solving Task

The purpose of this task is to help solidify students' understanding of signed numbers as points on a number line and to understand the geometric interpretation of adding and subtracting signed numbers. There is a subtle distinction between a fraction and a rational number. Fractions are always positive, and when thinking of the symbol ab as a fraction, it is possible to interpret it as a equal-sized pieces where b pieces make one whole.

Type: Problem-Solving Task

## Tutorial

In this example, we will work with three numbers in different formats: a percent, a decimal, and a mixed number.

Type: Tutorial

## Parent Resources

## Problem-Solving Task

The purpose of this task is to help solidify students' understanding of signed numbers as points on a number line and to understand the geometric interpretation of adding and subtracting signed numbers. There is a subtle distinction between a fraction and a rational number. Fractions are always positive, and when thinking of the symbol ab as a fraction, it is possible to interpret it as a equal-sized pieces where b pieces make one whole.

Type: Problem-Solving Task