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PS166 3 rd Grade Math Parent Workshop October 23 rd, 2014 Math Consultant: Nicola Godwin K-5 Math Teaching Resources LLC

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In Grade 3, instructional time focuses on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100 (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1) (3) developing understanding of the structure of rectangular arrays and of area (4) describing and analyzing two-dimensional shapes.

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Module 1 Properties of Multiplication & Division and Solving Problems with Units of 2-5 and 10 (25 days) Module 2 Place Value and Problem Solving with Units of Measure (25 days) Module 3 Multiplication & Division with Units of 0, 1, 6-9 and Multiples of 10 (25 days) Module 4 Multiplication And Area (20 days) Module 5 Fractions as Numbers on the Number Line (25 days) Module 6 Collecting and Displaying Data (10 days) Module 7 Geometry and Measurement Word Problems (40 days)

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April 22nd – April 24 th 2015 New York State Common Core Mathematics Test

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Basic multiplication and division facts are considered foundational for further advancement in mathematics. They form the basis for learning multi- digit multiplication and division, area, fractions, percentages, volume, ratios, and decimals. Everyday life skill/students need to be able to apply their knowledge of multiplication and division facts to real life problem solving situations.

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Content Standards related to multiplication and division Represent and solve problems involving multiplication and division 3.OA1 Interpret products of whole numbers, e.g. interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7. 2014 Released Question (1 point)

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3.OA2 Interpret whole-number quotients of whole numbers, e.g. interpret 56÷8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. 2013 Released Question (1 point)

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3.OA.2 2014 Released Question (2 points)

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3.OA3 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. **Grade 3 Standards focus on equal groups and arrays Students in Gd. 3 begin the step to formal algebraic language by using a letter for the unknown quantity in expressions or equations for one and two- step problems

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3.OA3 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. 2014 Released Question (1 point)

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3.OA32014 Released Question (2 points)

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3.OA.3 2014 Released Question (3 point question)

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3.OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 x?=48, 5 = ?÷3, 6x6 =?

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Understand properties of multiplication and the relationship between multiplication and division 3.OA5 Apply properties of operations as strategies to multiply and divide. Multiplication and division are inverse operations 8 x 3 = 24 24 ÷ 3 = 8 If 6x4=24 is known then 4x6=24 is also known (Commutative property of multiplication) 3x5x2 can be found by 3x5=15, then 15x2=30, or by 5x2=10, then 3x10=30 (Associative property of multiplication) Knowing that 8x5=40 and 8x2=16, one can find 8x7 as (8x5) + (8x2) = 40 +16 =56 (Distributive property)

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Strategy: Use the distributive property to decompose one factor 16 x 5 = (10 x 5) + (6 x 5) = 50 + 30 = 80 Try it: How could you break apart 22 x 9 to make it easier to multiply mentally?

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2014 Released Question (1 point) 3.OA.5 2013 Released Question (1 point)

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3.OA6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. 2013 Released Question (1 point) 2014 Released Question (1 point)

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Does your child demonstrate fluency? Is your child able to state answers to multiplication problems quickly without needing to count or use his/her fingers? Is your child able to make connections between facts? (e.g. if you know 10x7, how could you use this to help find the product of 9x7?) Is your child able to use his/her knowledge of multiplication facts to solve division facts? Being fluent with basic facts frees the brain to work on other math processes e.g. multiplication with three digit factors is time consuming, and often stressful, for students who must stop to figure out each basic fact along the way. Our goal is fluency with understanding. Without a foundation of understanding, memory can be very fleeting. Multiply and divide within 100 3.OA7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8x5=40, one knows 40÷5=8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

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Set REALISTIC Multiplication Goals 3 8 2 6 4 9 7 5 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 9 7 3 6 8 5 4 x 3 x 3 x 3 x 3 x 3 x 3 x 3 8 5 9 4 7 6 x 4 x 4 x 4 x 4 x 4 x 4 7 8 6 9 5 x 5 x 5 x 5 x 5 x 5 7 9 8 6 x 6 x 6 x 6 x 6 8 9 7 x 7 x 7 x 7 8 9 x 8 x 8 9 x 9 Instant recall of multiplication facts is not hard for most children but it does take practice. Instead of expecting children to learn all the facts at once break it down into manageable chunks. Start with only the 2’s. After students demonstrate instant recall of the 2’s, practice only the 3’s. When instant recall of the 3’s is demonstrated, practice the 2’s and 3’s together. Then move onto the 4’s etc. Be POSITIVE, encouraging and persistent. Remember: without the 0’s and 1’s there are only 36 single digit facts that have to be learned because the product of 3 x 5 is the same as the product of 5 x 3.

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Researchers have found that when the basic facts are treated as isolated bits of information and learned through rote drill, students have more difficulty remembering them. On the other hand, when students are given the opportunity to build relations among the facts they are better able to retain them (Dehaene 1999, Delazer 2005, Mysers & Thornton 1977). I can break 8x7 into (5x7) + (3x7) 35+21=56 If 10x7=70 then 8x7 is 70-14 or 56 8 x 7 The product of 8 x 7 is double the product of 4 x 7 because 8 is the double of 4 The product of 8x7 has to be an even number because an even number x an odd number always gives an even number. If 7x7 is a square number then 8x7 is one row (or column) of 7 more

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3.OA8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 2014 Released Question (1 point)

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3.OA9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends..

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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.

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2014 Released Question (3 points)

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3MD7c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of axb and axc. Use area models to represent the distributive property in mathematical reasoning. 2013 Released Question

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Standards for Mathematical Practice Models for multiplication and division Use precise vocabulary Array model Bar model Equal groups

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Short, ongoing routine that provides students with meaningful ongoing practice with mental computation to develop computational fluency. This morning you will see an Addition Number Talk focusing on the strategy Adding Up in Chunks. 53 + 36 = ? The teacher will present a problem written in horizontal format Students will figure our the answer mentally Students will share their answers Students will share their strategies The class will agree on the correct answer Steps 1-5 will be repeated for several problems

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More Sample Questions: https://www.engageny.org/resource/new-york-state-common-core-sample- questions NYCDOE information on the CCLS: http://schools.nyc.gov/Academics/CommonCoreLibrary/ForFamilies/LearningAtHome/SLH_ k8.htm http://schools.nyc.gov/Academics/CommonCoreLibrary/ForFamilies/LearningAtHome/SLH_ k8.htm Multiplication and division games to print and play at home: http://www,k-5mathteachingresources.com/3rd-grade-number-activities.html DO YOU HAVE ANY QUESTIONS?

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