### Examples

*Clarification 1:*Problem types are limited to length, area, weight, mass, volume and money.

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

**Grade:**7

**Strand:**Algebraic Reasoning

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

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- Area
- Capacity
- Customary Units
- Metric Units

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 6, students performed conversions within the same measurement system. In grade 7, students solve mathematical and real-world problems involving the conversion of units across different measurement systems. In grade 8, students will apply these conversions when solving problems involving the distance between two points in a coordinate plane.- Focus on using conversion ratios to create equivalent values.
- For example, if 1 foot = 12 inches, you can use the ratio of to solve problems.

- Students may also use conversion ratios in their science courses. Emphasize that multiplying by equivalent values of 1 does not change the value but gives an equivalent value in another unit of measurement.
- Instruction includes using manipulatives to estimate conversion ratios across measurement systems such as yard sticks, meter sticks, measuring cups and graduated cylinders
*(MTR.2.1).* - Students may need review on which units are used to measure length, volume and mass.
- Instruction includes using a reference sheet with conversion ratios.

### Common Misconceptions or Errors

- Students may incorrectly place the values in a conversion ratio. To address this misconception, have students estimate values prior to calculations using the conversion ratio
*(MTR.6.1).*

### Strategies to Support Tiered Instruction

- Teacher provides opportunities for students to comprehend the context or situation by engaging in questions (laminating these questions on a printed card for students to utilize as a resource in and out of the classroom would be helpful).
- What do you know from the problem?
- What is the problem asking you to find?
- Can you create a visual model to help you understand the problem?

- Teacher provides unit conversion sheet for students to determine the unit of measurement between different systems.
- Instruction focuses on using a unit conversion table to explicitly describe the process of converting between different units of measurement.
- Teacher provides instruction on color-coding and labeling the different units when setting up a proportional relationship to ensure corresponding units are placed in the corresponding positions within the proportion.
- Teacher encourages students to use their prior knowledge of proportions to convert unit of measurement across different measurement systems.
- Teacher provides students a visual of different units of measurements to compare and estimate the proper conversion ratio.
- Instruction includes the use of a three-read strategy. Students read the problem three different times, each with a different purpose (laminating these questions on a printed card for students to utilize as a resource in and out of the classroom would be helpful).
- First, read the problem with the purpose of answering the question: What is the problem, context, or story about?
- Second, read the problem with the purpose of answering the question: What are we trying to find out?
- Third, read the problem with the purpose of answering the question: What information is important in the problem?

- Teacher has students estimate values prior to calculations using the conversion ratio
*(MTR.6.1).*

### Instructional Tasks

*Instructional Task 1*

**(MTR.1.1, MTR.4.1)**Joe was planning a business trip to Canada, so he went to the bank to exchange $200 U.S. dollars for Canadian (CDN) dollars. On the way home from the bank, Joe’s boss called to say that the destination of the trip had changed to Mexico City. Joe went back to the bank to exchange his Canadian dollars for Mexican pesos. What is the value of Mexican pesos that Joe has now?

- Part A. What questions still need to be answered to approach this problem?
- Part B. The rates for CDN to the U.S. dollar and the rate of pesos to the CDN are shown below.
- Rate of $1.02 CDN per $1 U.S.
- Rate of 20.8 pesos per $1 CDN What is the value of Mexican pesos that Joe has now?

### Instructional Items

*Instructional Item 1*

Jia is buying strings of lights to hang on her patio deck. She needs 80 feet of lights to go around the entire patio, but the lights she wants to buy are only sold in packs of 5 meters. If one meter is approximately 3.28 feet, how many packs of lights will Jia need for her patio?

Instructional Item 2

**How many milliliters are in 12 fluid ounces?**

Instructional Item 3

Instructional Item 3

Convert 50 pounds to kilograms.

*Instructional Item 4*

When driving from London to Poland, the speed limit signs change from miles per hour (mph) to kilometers per hour (kph), but your rental car speedometer only reads in mph. If the speed limit on the highway is 100 kph, at what speed will you exceed the speed limit?

**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

## Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

## Tutorial

## STEM Lessons - Model Eliciting Activity

This Model Eliciting Activity (MEA) presents students with the real-world problem of contaminated drinking water. Students are asked to provide recommendations for a non-profit organization working to help a small Romanian village acquire clean drinking water. They will work to develop the best temporary strategies for water treatment, including engineering the best filtering solution using local materials. Students will utilize measures of center and variation to compare data, assess proportional relationships to make decisions, and perform unit conversions across different measurement systems.

## MFAS Formative Assessments

Students are asked to choose and justify the unit to be used in a formula and are asked to choose and explain the unit used in the answer.

Students are asked to find the approximate number of trees that are saved by using recycled paper.

## Student Resources

## Perspectives Video: Professional/Enthusiast

Get fired up as you learn more about ceramic glaze recipes and mathematical units.

Type: Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

Students are asked to determine the change in height in inches when given a constant rate of change in centimeters. The answer is rounded to the nearest half inch.

Type: Problem-Solving Task

In this task, students are presented with a real-world problem involving the price of an item on sale. To answer the question, students must represent the problem by defining a variable and related quantities, and then write and solve an equation.

Type: Problem-Solving Task

## Tutorial

In this lesson, students will be viewing a Khan Academy video that will show how to convert ratios using speed units.

Type: Tutorial

## Parent Resources

## Perspectives Video: Professional/Enthusiast

Get fired up as you learn more about ceramic glaze recipes and mathematical units.

Type: Perspectives Video: Professional/Enthusiast

## Problem-Solving Tasks

Students are asked to determine the change in height in inches when given a constant rate of change in centimeters. The answer is rounded to the nearest half inch.

Type: Problem-Solving Task

In this task, students are presented with a real-world problem involving the price of an item on sale. To answer the question, students must represent the problem by defining a variable and related quantities, and then write and solve an equation.

Type: Problem-Solving Task