EAST ALLEN COUNTY SCHOOLS

Bundle 4

Grade 6

Math

Big Idea: Interpretations Ratios and

Proportions

Enduring Understandings Essential Questions Part-whole relationships can be expressed in equivalent fraction, decimal, percent, or ratio forms. Mastery of proportional reasoning allows one to solve a variety of problems. Ratios and proportions are parts of a whole that can be represented in a variety of ways. Multiplication and division mastery is required when analyzing ratios and proportions.

What are different comparisons that can be made using ratios? How can ratios be used to find unknown quantities or inaccessible measurements? How are ratio, unit rate, and proportion related to real life occurrences? How does a proportion compare two equivalent ratios?

CC/Learning Targets Core Vocabulary Links to Technology 6.1.6 6.2.6 6.2.7

6.7 6.RP.3b 6.EE.7 6.EE.9

proportions unit rate

-Math!!! (app)

-Whiteboard (app) -Show Me (app) -SAS Flashcards (app)

Bundle Performance Task(s) The PTO in your school has decided to have the 6th graders publish a cookbook. There has been a decision to include 100 recipes, one on each page. This cookbook needs to be divided into three main sections: appetizers, main dishes, and desserts. Before you begin this task, you need to refer to other cookbooks to determine how many recipes are needed per category. If 20 recipes are used for dessert, the ratio would be 20:100, or in simplest form 1:5. You also need to explain how you determine the total amount of recipes in each category. Make a table including the following information: • Type of recipe • Ratio to total recipes • Number of recipes per category • Ratios represented in simplest form • Photographs evenly proportioned throughout cookbook • Three real example recipes must be included, with correct fractional measurements, such as 1/3 cup of sugar. As an extension, use DaVinci's ratio or Black Death .

Grade 6 Math Bundle 4

Quarter 2 Nov.-Dec.

Recommended Read-Alouds

L.A. Bundle 4 Read-Alouds

Page 2 of 4

Big Idea: Interpretations

Title Author Relates to…

Chasing Vermeer Blue Balliett Patterns

Extreme Temperatures: Learning About Positive and Negative Numbers John Strazzabosco Temperatures

If You Hopped Like A Frog David Schwartz Ratios and Proportions

Jim and the Beanstalk Raymond Briggs Proportions

Math G6 - Bundle 4

CC/Learning Targets Resource of Ideas Evidence of Learning 6.1.6

Model ratios using objects, drawings, or other concrete or pictorial representations.

-If You Hopped Like A Frog by David Schwartz (ratios/proportions) -Jim and the Beanstalk by Raymonf Briggs (ratio/proportions) -Ratio!!! (apps) (Now costs $3.99) -Ratio of Golden Rectangle (play spiral, measure ratio) -Holt Math Hands-On Lab pp. 396-397

-Models to represent ratios -Calculating ratios of height to width in famous architecture

6.2.6

(6.PR.1)

(6.RP.2) (6.RP.3)

a. Define ratio using the notations: a/b, a to b, a:b.

b. Interpret ratios to represent the relative size of two quantities. Include situations involving part to part (girls to boys) and part to whole (girls to total students). Connect part to whole situations to prior work with fractions.

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.”

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

-Holt Middle School Math, Lessons 8-1, 8-2, 8-3, 8-4, 8-5, 8-6 -Unit rates -Finding Unit Rates (video from Khan Academy) -Unit Rate using IXL Activity (could be an assessment) - Holt Middle School Math, pp. 392-395

-Holt Math Corresponding Lesson Resources -Unit Rate using IXL Activity

Math G6 - Bundle 4

cups of sugar, so there is ¾ cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”

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 equations1.

b. 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? (Notes: The CCSS includes unit rates, the use of tables and the coordinate plane with ratios, solving problems involving finding the whole given a part and the percent, using ratio reasoning to do measurement conversions, and manipulating and transforming units)

6.2.7 a. Define proportion. Connect proportions to prior work with equivalent fractions. b. Write proportions based on problem situations, using a variable as the unknown.

c. Solve problems involving proportions. Solve proportions mentally (connecting to the concept of equivalent fractions) as well as solving for the unknown using an equation.

-If You Hopped Like A Frog by David Schwartz (ratios/proportions) -Jim and the Beanstalk by Raymonf Briggs (ratio/proportions) -Proportional triangles lesson (interactive practice at bottom of page) -Proportions lesson (interactive practice at bottom of page) -Holt Middle School Math, Lessons 8-2, 8-3, 8-4, 8-5, 8-6, 11-2 -Holt Hands-On Lab, pp. 396-397

-Holt Math Corresponding Lesson Resources -Proportional triangles quiz (interactive) -Proportions quiz (interactive) -Calculate proportions of houses or local buildings

Math G6 - Bundle 4

6.7 Problem Solving -The Problem Solver 6: Activities for Learning Problem-Solving Strategies -Five Easy Steps to a Balanced Math Program for Secondary Grades pp.29-73 -Math Curse by Jon Scieszka (problem solving)

-Problem Solver Activities -See Problem Solving Template in Appendix.

6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

-Holt Middle School Math, pp. 604-605 -Problem Solver Activities -See Problem Solving Template in Appendix.

6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

-Variables (independent/dependent)

-Variables video

-Problem Solver Activities -See Problem Solving Template in Appendix.

Math G6 - Bundle 4

Correlating CC/Learning Targets Teacher Notes

6.1.7 6.2.4 6.3.1

6.3.2 6.5.10

-Due to ISTEP, probability, mean, mode, median and range need to be incorporated into DMR and Problem Solving. These are yellow standards addressed in Bundle 8. -Problem Solving indicators need to be embedded in each Bundle -Nlvm.usu.edu (huge library of virtual manipulatives for all standards!) -Studyzone.com (huge library of process and content activities; many are interactive) -Onlinemathlearning (huge library of online videos for all standards)

-Study Jams (huge resource of interactive lessons and activities) -Five Easy Steps to a Balanced Math Program for Secondary Grades, pp. 75-100 -All embedded apps included in this curriculum are free.