6.4

6.4 is a knowledge and skills statement. These are the student expectations under it.

• 6.4.A

  compare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multipl...

• 6.4.B

  apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates

• 6.4.C

  give examples of ratios as multiplicative comparisons of two quantities describing the same attribute

• 6.4.D

  give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients

• 6.4.E

  represent ratios and percents with concrete models, fractions, and decimals

• 6.4.F

  represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and ...

• 6.4.G

  generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money

• 6.4.H

  convert units within a measurement system, including the use of proportions and unit rates

01

What Students Need to Do

Students decide whether a situation follows an additive rule or a multiplicative rule. They use ratios and rates to compare quantities, make predictions, and solve problems. They also move among fractions, decimals, percents, models, and measurement units.

02

What Mastery Looks Like

Students can identify additive and multiplicative rules from words, tables, equations, and graphs. They can find equivalent ratios, unit rates, fractions, decimals, and percents, then use them to compare options or predict values. Their unit conversions are reasonable and include correct labels.

03

Common Misconceptions

Students often treat every relationship as additive, especially when values increase by a steady amount. They may reverse a ratio, confuse a rate with a ratio, or move the decimal incorrectly when converting percents. They may also multiply when converting to a smaller unit instead of checking whether the answer should increase or decrease.

04

How to Assess It

Exit ticket: A drink mix uses 3 cups of water for 2 packets, and shipping adds $3 to an order. Write each rule, label it additive or multiplicative, find the water needed for 5 packets, express 3/4 as a decimal and percent, and convert 2 cups to fluid ounces using 1 cup = 8 fluid ounces.

1. 01

   Shade 10%, 25%, 50%, and 75% on laminated 10 by 10 grids, then match each model to fraction and decimal cards.

2. 02

   Ask students to explain why y = 4x is multiplicative while y = x + 4 is additive, using tables and graphs.

3. 03

   Run a card sort matching ratio statements, unit rates, fractions, decimals, percents, equations, tables, and graphs.

4. 04

   Use grocery ads to compare unit prices, calculate a percent discount, and decide which package is the better buy.

• 7.4

  The student applies mathematical process standards to represent and solve problems involving proportional relationships

• 7.5

  The student applies mathematical process standards to use geometry to describe or solve problems involving proportional relationships

• 6.5

  The student applies mathematical process standards to solve problems involving proportional relationships

• 7.6

  The student applies mathematical process standards to use probability and statistics to describe or solve problems involving proportional relationships