In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.
Understand ratio concepts and use ratio reasoning to solve problems.
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.”
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Understand (Concept of Ratio)
3 - Use (Ratio language)
2 - Describe (Ratio relationship)
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2 - I understand the concept of a ratio.
3 - I can use ratio language to describe a ratio relationship.
2 - I can describe a ratio relationship between two quantities.
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A. Relationships between two quantities can be described using the ratio concept and its language.
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A.1 What is a ratio?
A.2 What vocabulary words are involved in ratio language?
A.3 How does one describe the relationship between two quantities in a ratio?
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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.”
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Ratio
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2 - Understand (Concept of Unit rate)
3 - Use (Rate language)
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2 - I understand the concept of a unit rate.
3 - I can use rate language in context of a given ratio.
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A. One can convert a ratio relationship to a unit rate and can use rate language to explain the relationship between them.
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A.1 What is a unit rate?
A.2 How does one convert a ratio relationship into a unit rate?
A.3 What vocabulary is involved in unit rate language?
A.4 How does one use rate language in context of a given ratio?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Problems
Problem types e.g.
Tables [a]
Plane [a]
Problems [b] e.g.
Reasoning [d]
Units [d]
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3 - Use (Rate reasoning)
3 - Use (Ratio reasoning)
3 - Solve (Real world problems)
3 - Solve (Mathematical problems)
6 - Make (Tables [a])
4 - Relate (Quantities [a])
2 - Find (Missing values [a])
3 - Plot (Pairs of values [a])
3 - Use (Tables [a])
4 - Compare (Ratios [a])
3 - Solve (Unit rate problems [b])
2 - Find (Percent [c])
3 - Solve (Problems [c])
2 - Find (Whole [c])
3 - Use (Ratio reasoning [d])
3 - Convert (Measurement units [d])
2 - Multiply (Quantities [d])
2 - Divide (Quantities [d])
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3 - I can use rate reasoning.
3 - I can use ratio reasoning.
3 - I can solve real world problems involving ratios and rates.
3 - I can solve mathematical problems involving ratios and rates.
6 - I can make a table of equivalent ratios. [a]
4 - I can relate quantities with whole number measurements. [a]
2 - I can find missing values in a table. [a]
3 - I can plot pairs of values on the coordinate plane. [a]
3 - I can use tables. [a]
4 - I can compare ratios by using tables. [a]
3 - I can solve unit rate problems. [b]
2 - I can find the rate of a quantity if given the percent of a quantity. [c]
3 - I can solve problems involving wholes, parts and percentages. [c]
2 - I can find the whole if I have been given a part and the percent. [c]
3 - I can use ratio reasoning. [d]
3 - I can convert between units of measurement. [d]
2 - I can multiply quantities. [d]
2 - I can divide quantities. [d]
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A. Reasoning is required to solve real world or mathematical problems involving ratios and rates.
B. Real world and mathematical problems involving ratios and rates can be solved by using tables and graphs.
C. Many real world problems can be solved by using unit rates.
D. When given a part and a percent, one can find the whole after converting the percent to a rate.
E. One can solve real world or mathematical problems involving ratios and rates by using reasoning.
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A.1 What reasoning can one use involving rates or ratios?
A.2 What real world problems can be solved by using rates or ratios?
A.3 How does one solve real world problems using reasoning?
A.4 How does one solve mathematical problems using reasoning?
A.5 What is an equation?
B.1 How does one design a table?
B.2 What are equivalent ratios?
B.3 What are whole numbers?
B.4 How does one relate quantities with whole number measurements?
B.5 How does one find missing values in a table?
B.6 How does one plot pairs of values on the coordinate plane?
B.7 How does one use a table to compare ratios?
C.1 What is a unit rate?
C.2 How do you solve unit pricing problems?
C.3 How do you solve constant speed problems?
D.1 How does one change the percent of a quantity into a rate?
D.2 What do the terms whole, part and percent mean?
E.1 How does one solve problems involving wholes, parts and percentages?
E.2 How does one convert between different units of measurement?
E.3 How does one multiply and divide quantities?
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