Embedded Files
Chapter Overview
Chapter Overview
In Chapter 5, students will develop a conceptual understanding of and strategies for multiplying fractions and decimals. They also develop strategies and rules for finding the area of non-rectangles, specifically, various quadrilaterals and triangles, and learn to find the area of complex shapes.
Section 5.1 looks at multiplication of fractions, decimals, and mixed numbers. The lessons begin with geometric representations: dividing whole figures into parts, and then further dividing them, calculating “parts of parts” to find the product. Students then generalize this process to develop an algorithm for multiplying fractions.
Multiplying with mixed numbers and fractions greater than one is then introduced. Students learn to use generic rectangles to organize multiplication of mixed numbers. They also convert mixed numbers to fractions greater than one and apply their algorithm. In Section 5.2, students look at multiplying decimals, making sense of the expected size of a product, and thus the placement of the decimal point.
Standards for Mathematical Practice
Standards for Mathematical Practice
In Chapter 5, students will be using various tools to look for and make use of the mathematical structures when multiplying fractions, decimals, and mixed numbers, and when calculating areas of non-rectangular shapes.
Even when not mentioned specifically for a lesson, encourage abstract and quantitative reasoning, the construction of viable arguments and critiquing the reasoning of others, and attention to precision in team discussions. The overarching goal of Chapter 5 is to make sense of problems and persevere in solving them.
CA Content Standards
CA Content Standards
6.NS.1. (in 6.1) Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
6.RP.3c. 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.
6.NS.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
6.G.1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
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