Sixth Grade Math Domain: Ratios and Proportional Relationships Cluster: Understand ratio concepts and use ratio reasoning to solve problems.

Sixth Grade Math

Domain: Ratios and Proportional Relationships Cluster: Understand ratio concepts and use ratio reasoning to solve problems.

Common Core Standard: 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship

between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2

wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

Essential Vocabulary Task Analysis Learning Activities/Assessments Resources

Prior

 Fraction

 Quantity

 Compare

 Measure

Explicit

 Ratio

 Part-to-part

 Part-to-whole

 Colon

 Relationship

Introductory

 Rate

 Unit Rate

 Proportion

 Compare two quantities or measures.

 Display a ratio or a comparison as a part and a part-to-whole relationship using the correct mathematical symbols (e.g. words, fraction bar, and colon).

 Define a ratio.

 Identify and describe any ratio using “For every _____ ,there are _____”

 Understand the concept of a ratio and use ratio language to

describe a ratio relationship between the quantities

 M&M Ratios (CGW, CT)

 Intro to Ratios (S, Q)

 Number CSI (CGW, CT)

o Includes ratios, operations with decimals, comparing fractions, and time

 Illuminations Bean Counting

 Learn Zillion (ratio language)

Sixth Grade Math

Domain: Ratios and Proportional Relationships Cluster: Understand ratio concepts and use ratio reasoning to solve problems.

Common Core Standard: 6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use

rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar,

so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.

Essential Vocabulary Task Analysis Learning Activities/Assessments Resources

Prior

 Reciprocal

 Ratio

Explicit

 Per

 Reciprocal

 Rate

 Unit rate

 Part-to-one

 Relationship

 Simplify

 Simplest form

Introductory

 Proportion

 Name the amount of either quantity in terms of the other quantity (150 miles: 2hrs OR 2hrs:150 miles).

 Identify appropriate symbols for expressing unit rate (non-equal ≠, fraction bar, colon)

 Define a part to one relationship (unit rate).

 Calculate (re-write) a ratio as a unit rate.

 Explain how related unit rates are reciprocals.

 Explain why b ≠ 0.

 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.

 Let’s Go On a Ride (GCW, CT, Q) o Introductory Activity

 Math Snacks

o Activities, videos, and lessons aligned with Common Core (covers 6.RP.1-3)

 Usain Bolt Video o Use as an

introduction to finding unit rate (i.e. how many m/sec)

Sixth Grade Math

Domain: Ratios and Proportional Relationships Cluster: Understand ratio concepts and use ratio reasoning to solve problems.

Common Core Standard: 6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by

reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

A.

B.

C.

D.

Essential Vocabulary Task Analysis Learning Activities/Assessments Resources

A. Prior

 Coordinate plane

 Ordered pairs

 X and y axis

 X and y coordinates

 Patterns

 Sequences

A.

 Read a table to find a ratio.

 Apply properties of multiplication and division to find missing values.

 Create a table with given information and fill in missing values.

 Word Problem Cards (CGW)

o Cut out and laminate cards; have students use dry erase markers to answer

questions on cards o Have students work in

partners/groups to

complete questions. When

 Extra Practice

 Learn Zillion (using ratios tables)

 Learn Zillion (converting measures)

 Learn Zillion (percents)

 Yummy Math

 Quadrant

Explicit

 Equivalent ratios

 Equation

 Function table

 Rule

 Table



Unit rate

 Proportional reasoning

B.

Prior

 Equivalent ratio

 Unit rate

 Value

 Decimal

 Fractions

Explicit

 Value

 Constant speed

 Unit pricing

 Decimal

 Real world

 Unit rate

Introductory  Proportional reasoning

C.

Prior

 Hundreds grid

 Fraction

Explicit

 Write the rule for a table (equation)

 Plot ratios as ordered pairs on the coordinate plane.

 Apply the rule or equation to justify the solution.

 Find a pattern and calculate a new value when the ratio remains the same.**

 Students use ratios, unit rates and multiplicative reasoning to solve problems in various

contexts, including measurement, prices, and geometry.

B.

 Identify key details to accurately solve a word problem.

 Plan and construct the steps to solve for the unit rate and determine the new value.

 Recognize that unit rates can be represented as a whole number, a fraction, or a decimal.

 Use an equivalent ratio to find missing values.

 Use fractions and decimals as unit rates to solve real world

problems (e.g. recipes, constant speed, unit pricing, geometry).

 Solve unit rate problems including those involving unit pricing and constant speed.

C.

 Define a percent as a rate per 100.

 Model a percent on a hundreds grid.

 Recognize that the whole is being divided into 100 equal parts.

they are done, pass cards around until all groups have answered all 6 cards (similar to carousel).

 Review Basketball (CGW, Q)

 Ratio Blaster (S, Q, WTL)

 World Series of Pop Culture (CGW, CT, Q)

 Neighborhood Snow Removal (CGW, CT, Q)

 NHL Activity (CGW, Q)

 Intro to Percents Smart Notebook o To download, select

“Percents” under, “Math 6 Notebook Files”

 Ratios and Proportions Assessment

 Real World Tasks

 Challenging Practice

 Fraction, Decimal, Percentage equivalents and Challenge

 Tape diagram

 Model

 Percent

 Per 100

 Percent bar (%)

 Quantity

Introductory

 Sales Tax

 Interest

 Discount D.

Prior

 Metric (and related unit vocabulary)

 Customary (and related unit

vocabulary)

 Conversion

 Measure

 Powers of ten

 Decimal

 Fraction

 Units

Explicit

 Unit

measurements

 Equivalent ratios

 Conversion factors

.

 Use ratios to identify percent as a rate per 100.

 Model percent of a quantity using a hundreds grid.

 Model the percent of a quantity using a tape diagram.

 Represent a percent of a quantity as a number with a percent bar.

 Calculate the percent of a quantity using the algorithm

 Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems

involving finding the whole, given a part and the percent.

D.

 Represent equivalent measurements as ratios.

 Compare unit measurements through the use of equivalent ratios (e.g. if 4 cups = one quart, then 12 cups =? quarts).

 Define conversion factor as a fraction equal to 1 since the numerator and denominator describe the same quantity, e.g. 12 inches 1 ft