7.RP.1 - About the Math, Learning Targets, and Rigor

Grade 5 GT Ratio and Proportions

7.RP.1

About the Math

Full Standard

Analyze proportional relationships and use them to solve real-world and mathematical problems. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction ^1/2/_1/4 miles per hour, equivalently 2 miles per hour

Measurement Topic

This standard is reported on the report card in these quarters as follows:

**5th Grade Students Learning 5 G/T Standards**
Quarter 1	Quarter 2	Quarter 3	Quarter 4
Report Card Measurement Topic: Demonstrates understanding of number, fraction, and decimal concepts.

Learning Targets (I can)

Explain what a unit rate is.
Identify common unit rates in the real world.
Estimate unit rates (e.g. 4 oranges for 30¢ is about 7¢ per orange).
Find unit rates associated with ratios of fractions in like or different units.
Compare unit rates to solve real-world problems.
Use unit rates to solve real-world problems.

About the Math

Explain what a unit rate is.
Identify common unit rates in the real world.
Estimate unit rates (e.g. 4 oranges for 30¢ is about 7¢ per orange).
Find unit rates associated with ratios of fractions in like or different units.
Compare unit rates to solve real-world problems.
Use unit rates to solve real-world problems.

Knowledge of ratios and unit rates is extended and a development of understanding proportionality is introduced. A ratio is an expression which compares separate quantities relative to each other, and typically involves exactly two quantities. Measurements can include: time, frequency, distance, length, weight, mass, area, etc. Unit rates are a type of ratio that relates to a quantity to 1 unit. Complex fractions will be used to express ratios related to a unit rate. For example, $\frac{1}{2}$ $\frac{1}{2}$ teaspoon per $\frac{1}{3}$ $\frac{1}{3}$ cup can be expressed as $\frac{1 / 2}{1 / 3}$ $\frac{1/2}{1/3}$ per cup, or $\frac{1 / 2}{1 / 3}$ $\frac{1/2}{1/3}$ $/$ $\slash$ 1. Ratios that are equivalent have the same unit rate, so they are proportional. The relationship between the quantities is proportional if the numerator and denominator can both be multiplied or divided by the same unit. A proportion is an equation with a ratio on each side. Proportional relationships from other relationships are explored by utilizing multiple representations including tables and equations.

Essential vocabulary for this standard includes: ratio, complex fraction, equivalent fractions, units, unit rate, unit conversions, double number line, equation, simplify. Visit the online dictionary (Links to an external site.) Links to an external site. or visual math dictionary (Links to an external site.) Links to an external site. for vocabulary support.

Progression of Standard within Grade 5 GT

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1	Quarter 2	Quarter 3	Quarter 4
Explain what a unit rate is. Identify common unit rates in the real world. Estimate unit rates (e.g. 4 oranges for 30¢ is about 7¢ per orange). Find unit rates associated with ratios of fractions in like or different units. Compare unit rates to solve real-world problems. Use unit rates to solve real-world problems.

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 6	HS
Understand unit rate (6.RP.2)	Use units as a way to understand problems and to guide the solution of multi-step problems (HS.N-Q.A.1)

Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction.

If Layla can run 150 feet in 1/3 of a minute. What is her unit rate in feet per minute?
A worm can crawl 6 feet 8 inches in 1 ½ hour. What is the worm's unit rate?
A work crew can pave ¾ of a mile of the interstate in 6 ¾ hours. What is their unit rate for paving the interstate?
Determine the best buy between two brands or two sizes of a single brand.
Calculate the mileage comparison of different vehicles.

SLIDE-BASED TASKS

These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 3 • Unit Rate

Compute and Find Unit Rates to Solve Real-World Problems with Unit Rates:

Additional Tasks

These links provide instructional ideas connected to this standard. [NOTE: NCTM membership required for access to Illuminations lessons.]

Cider Versus Juice - Variation 1 Links to an external site.(Illustrative Math)
Cider Versus Juice - Variation 2 Links to an external site. (Illustrative Math)
Cooking with the Whole Cup Links to an external site.(Illustrative Math)
Molly’s Run Links to an external site. (Illustrative Math)
Molly’s Run Assessment Variation Links to an external site.(Illustrative Math)
Track Practice Links to an external site.(Illustrative Math)
Gas Station Rip-Off Links to an external site. (Dan Meyer 3-Act Task)
Graduation Links to an external site. (Dan Meyer 3-Act Task)
Apple Pie Bake Sale Download Apple Pie Bake Sale
(HCPSS)
Camping Trip Download Camping Trip
(HCPSS)
Hair and Nail Growth Download Hair and Nail Growth
(HCPSS)
Olympic Track Athlete Download Olympic Track Athlete
(HCPSS)
Party Planning Download Party Planning
(HCPSS)
Reading Assignment Download Reading Assignment
(HCPSS)
Feeding Frenzy Links to an external site. (NCTM, Illuminations)
Who Lost More Links to an external site. (NCTM, Illuminations)

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.

Print Resources
Book Title	Grade	Pages
Groundworks Reasoning with Numbers	6	p. 32-39
Groundworks Reasoning with Numbers	7	p.32- 39 p.40-47
Teaching the Common Core Math Standards with Hands-On Activities	6-8	p.81- 83
Math Course 2 Teacher Edition	7	p. 404- 408

Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

Assessment

Learning Targets

rubric

Explain what a unit rate is.
Identify common unit rates in the real world.
Estimate unit rates (e.g. 4 oranges for 30¢ is about 7¢ per orange).
Find unit rates associated with ratios of fractions in like or different units.
Compare unit rates to solve real-world problems.
Use unit rates to solve real-world problems.

Learning targets identify what students should be able to do. The resources below can be used to measure student understanding of the standard. This rubric can be applied to tasks and observations for assessment and/or grading.

Rubric for Tasks Links to an external site.

Visit the SBIR (Standards Based Instruction and Reporting) tab in Course Essentials for more information and clarification. There you will find the measurement topic crosswalk, report card comments, links to professional learning/resources and guidance.