enVision Mathematics Topics 5-6
6th Grade; January – February (7 weeks); 3rd Quarter
Embedded Files
Topic Title(s):
Understand and Use Ratio and Rate (Topic 5)
Understand and Use Percent (Topic 6)
Prepared Graduates:
MP2. Reason abstractly and quantitatively.
MP3. Construct viable arguments and critique the reasoning of others.
MP7. Look for and make use of structure.
Standard(s):
1. Number and Quantity
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
6.RP.A. Ratios & Proportional Relationships: Understand ratio concepts and use ratio reasoning to solve problems.
Apply 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.” (CCSS: 6.RP.A.1)
Apply 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.” (Expectations for unit rates in this grade are limited to non-complex fractions.) (CCSS: 6.RP.A.2)
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. (CCSS: 6.RP.A.3)
Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. (CCSS: 6.RP.A.3.a)
Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? (CCSS: 6.RP.A.3.b)
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. (CCSS: 6.RP.A.3.c)
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. (CCSS: 6.RP.A.3.d)
Use ratio tables to test solutions and determine equivalent ratios. (Entrepreneurial Skills: Critical Thinking/Problem Solving)
Analyze and use appropriate quantities and pay attention to units in problems that require reasoning with ratios. (MP2)
Construct arguments that compare quantities using ratios or rates. (MP3)
Use tables, tape diagrams, and double number line diagrams to provide a structure for seeing equivalency between ratios. (MP7)
Inquiry Questions
How are ratios different from fractions?
What is the difference between a quantity and a number?
How is a percent also a ratio?
How is a rate similar to and also different from a unit rate?
Coherence Connections
This expectation represents major work of the grade.
In prior grades, students work with multiplication, division, and measurement. Prior knowledge with the structure of the multiplication table is an important connection for students in creating and verifying equivalent ratios written in symbolic form or in ratio tables (multiplicative comparison vs. additive comparison).
In Grade 6, this expectation connects with one-variable equations, inequalities, and representing and analyzing quantitative relationships between dependent and independent variables.
In Grade 7, students analyze proportional relationships and use them to solve real-world and mathematical problems. In high school, students generalize rates of change to linear and nonlinear functions and use them to describe real-world scenarios.
Academic Vocabulary & Language Expectations:
Ratio, terms, circumference, diameter, equivalent ratios, Pi, rate, unit rate, unit price, constant speed, conversion factor, dimensional analysis, percent
Assessments:
Instructional Resources & Notes:
enVision Mathematics Topics 5-6
Let's Investigate! Tasks
Let's Investigate! Playing Fair (TE) (relates to Lesson 5-4)
Let's Investigate! Rate That Scooter (TE) (relates to Lesson 5-6)
Let's Investigate! Straight from the Headlines (TE) (relates to Lesson 6-2)
Let's Investigate! Per Sense (TE) (relates to Lesson 6-5)
5th-to-6th Grade Warm-Ups for Activating Prior Knowledge (Geoff Krall)
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention Topic 5: Understand Ratios, Find Equivalent Ratios, Use Ratio Tables to Solve Problems, Visualize Rate
Tier 1 Intervention Topic 6: Finding Percents, Find the Whole from a Part and a Percent
Coherence Map/Concept Progressions: 6.RP.A.1, 6.RP.A.3.a, 6.RP.A.3.b, 6.RP.A.3.c, 6.RP.A.3.d
enVision Mathematics 6-8 & Number Worlds Connections (for SVVSD Special Education teachers only)
Page updated
Report abuse