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Common to the Core - C2tC A Glenn County Professional Development Day September 23, 2013

Common to the Core - C2tC A Glenn County Professional Development Day September 23, 2013. What Does Multiplication Look Like? Grades 3–5 Katy Early, CSU Chico Mathematics Project kearly@csuchico.edu. Mental Math Warm-Up!. 13 x 22 =

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Common to the Core - C2tC A Glenn County Professional Development Day September 23, 2013

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  1. Common to the Core - C2tCA Glenn County Professional Development DaySeptember 23, 2013 What Does Multiplication Look Like? Grades 3–5 Katy Early, CSU Chico Mathematics Project kearly@csuchico.edu

  2. Mental Math Warm-Up! 13 x 22 = As you solve this multiplication, think about your own thinking. • What approach(es) did you use? • Why did you choose that method? • Are there any other ways you could solve it? • How will you explain your method to others? • Does your method attend to place value? How or why not? • How will you know whether your answer is correct?

  3. Standards for Mathematical Practice • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning.

  4. Picturing Multiplication from 3rd grade through Algebra

  5. Sketch a picture to illustrate2 × 3 = 6 What is another way to illustrate 2 × 3 = 6 ?

  6. What language explains how your pictures show 2 × 3 = 6?

  7. How do children picture multiplication? •  •  •  •  •  • 

  8. Focus Standards for Picturing Multiplication 3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

  9. Moving beyond groups of… • Our pictures of 2 × 3 all work well for third grade standards. • How do they work at grades 4, 5, and beyond? • Picturing 6 × 5 as 6 equal groups of 5 makes sense and is relatively easy to illustrate. • Picturing 6 × 50 as 6 equal groups is not so easy! • 3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

  10. Six groups of fifty:

  11. Recording multiplication methods How do Common Core standards expect students to record their multiplication methods? 4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. On paper, multiply 12 x 14, using whatever calculation method you know best.

  12. Building multiplication rectangles • With a partner, build a rectangle with dimensions 12 × 14. • What language describes the rectangle as a multiplication problem? • 12 rows of 14 • 12 groups of 14 • the area of a 12 × 14 rectangle • Where is the 12? Where is the 14? Where is the product?

  13. What multiplication is illustrated here?

  14. ThePartial Products algorithm allows students to use strategies based on place value, as required by CCSS.

  15. Practice by building some more rectangles! • 3 × 22 • 13 × 22 • Take one flat, five rods and six small cubes. Build a multiplication rectangle. What are the factors? What is the product? Record your multiplication rectangle with a picture and with calculations.

  16. Picturing Multiplication of Fractions

  17. How can we picture multiplication of fractions? 5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

  18. How can we illustrate ½ × ⅓ ? • Will groups of ⅓ work? • Will an array work? • Will a rectangle work? • Try drawing a picture of ½ × ⅓.

  19. There are many on-line resources to support CCSS implementation! • Illustrative Mathematics: http://www.illustrativemathematics.org/pages/fractions_progression • California Mathematics Council: http://www.cmc-math.org/ • Butte County Office of Education, Educational Support Services Division: http://www.bcoe.org/cms/One.aspx?portalId=757608&pageId=1011864

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