Fractions and Ratios Big Idea: Rational numbers can be used to describe ratios and proportional relationships, and specific properties govern operations with rational numbers.
Umbrella Essential Teacher Question:Can students make sense of, solve, and operate with rational numbers that represent quantities and comparisons?

Umbrella Essential Question Student:Can I make sense of, solve, and multiply and divide fractions, decimals, and percents in word problems (including probability and counting problems)?

Suggested Instructional Time:9 weeks

Multiplication and Division of Fractions, Decimals, and Percents Big Idea: Understanding the relationship and converting between fractions, decimals, and percents. Multiplying and dividing decimals and fractions.
Essential Teacher Question:Can students determine the equivalence and operate with rational numbers in context?

Essential Question Student: Can I use equivalence to help me solve problems that require multiplying and dividing fractions, decimals and percents?

Suggested Instructional Time: 6 Weeks

Strand Concept

Mathematical Practices

Formatives

G6S1C1PO 2: Use prime factorization to express a whole number as a product of its prime factors and determine the greatest common factor and least common multiple of two whole numbers

5.NF.4a: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Interpret the product () q as a parts of a partition of q into bequal parts; equivalently, as the result of a sequence of operations aq÷b. For example, use a visual fraction model to show () 4 = , and create a story context for this equation. Do the same with () () = ^{8}/_{15}. (In general, () () = .)

MP. 1 Make sense of problems and persevere in solving them
MP.7. Look for and make use of structure

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5.NF.7: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.)

Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for () ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that () ÷ 4 = because () 4 = .

b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4÷() = 20 because 20 () = 4.

c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share lb of chocolate equally? How many -cup servings are in 2 cups of raisins?

5.MP.1. Make sense of problems and persevere in solving them. 5.MP.7. Look for and make use of structure. 5.MP.8. Look for and express regularity in repeated reasoning.

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G6S4C4PO 3: Estimate the measure of objects using a scale drawing or map.

MP. 1 Make sense of problems and persevere in solving them
MP. 2 Reason abstractly and quantitatively
MP. 5 Use appropriate tools strategically

Probability and Counting Big Idea: Describing and exploring probability using the multiplication principle and systematic listing. Representing probability using fractions, decimals, and percents in context.
Essential Question Teacher: Can students use rational numbers to explain and solve ratio and counting problems?

Essential Question Student: Can I use fractions, decimals, and percents to explain and solve ratio and counting problems?

Suggested Instructional Time: 3 Weeks

Strand Concept

Strand Concept

Mathematical Practices

Formatives

S2C2PO 2: Explore probability when performing experiments by:

Comparing outcomes of the experiment to predictions

Comparing the results of multiple repetitions of the experiment

S2C2PO 1: Describe the theoretical probability of events and represent the probability as a fraction, decimal, and percent.
G6S2C2PO 1: Use data collected from multiple trials of a single event to form a conjecture about theoretical probability.

MP. 3 Construct viable arguments and critique the reason of others
MP. 5 Use appropriate tools strategically

S2C3PO 1: Analyze relationships among representations and make connections to the multiplication principle of counting.

S2C3PO 2: Solve a variety of counting problems and explain the multiplication principle of counting.

G6S2C2PO 3: Determine all possible outcomes (sample space) of a given situation using a systematic approach.

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G6S2C3PO 2: Explore counting problems with Venn Diagrams using 3 attributes.

MP. 3 Construct viable arguments and critique the reason of others
MP. 5 Use appropriate tools strategically
MP. 8 Look for and express regularity in repeated reasoning