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| In this unit, children relate their part-whole understanding of fractions to visual and symbolic representations, including standard notation, and begin to explore fraction equivalence. They also develop multiplication fact strategies by working from their understanding of multiplication and known facts to find unfamiliar products by using arrays, area models, and properties of multiplication. The following big ideas will be covered in this unit: - The number above the bar in a fraction is the counting number. It tells how many parts we have. It is called a numerator. The number below the bar tells what is being counted. It tells you the fractional part that is being counted. - When two fractions are equivalent that means there are two ways of describing the same amount by using different sized fractional parts. - There are patterns and relationships in basic facts. You can figure out new or unknown facts from the ones you already know. - - The Distributive Property can be used to figure out new or unknown facts. Factors can be decomposed to generate two facts that are easier to solve. This can be shown by breaking apart an array. |
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| Operations & Algebraic Thinking 3.OA.A. Represent and solve problems involving multiplication and division. e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ÷ 3, 6 × 6 = ?. 3.OA.B. Understand properties of multiplication and the relationship between multiplication and division. Students need not use formal terms for these properties.
Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3
× 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. 3.OA.C. Multiply and divide within 100. 3.OA.C.7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 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. 3.OA.D. Solve problems involving the four operations, and identify and explain patterns in arithmetic. 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. Number & Operations—Fractions Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8. 3.NF.A.1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. 3.NF.A.3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. 3.NF.A.3b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. 3.NF.A.3d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. 3.MD.C. Geometric measurement: understand concepts of area and relate area to multiplication and to addition. 3.MD.C.7c. 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 a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. 3.G.A. Reason with shapes and their attributes. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. | Students will have opportunities to: Make sense of multiplication and division problems and persevere in solving them (MP. 1) Attend to precision by moving from less sophisticated strategies to more efficient strategies for solving multiplication problems (MP. 6) Use clear and precise language such as numerator, denominator, and fraction with increasing precision to discuss their reasoning (MP. 6) Look for and make use of structure when working with fact families (MP. 7)
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| - Fractional parts are equal shares or parts of a whole or unit. - Multiplication is related to addition and involves counting groups of like size and determining how many there are in all. - Models such as an array is used to represent multiplication. - There are patterns in multiplication, such as you can multiply factors in any order, you will get the same product. - Division can be interpreted as fair sharing or as repeated subtraction. - Multiplication and division have an inverse relationship. | -Fractions greater than, less than, and equal to one can be represented on the number line. - Fractions can be compared using benchmark fractions and visual models such as the area model and number lines. Equivalent fractions name the same point on a number line. - A ruler is a measurement tool that can be partitioned into fractional parts for precise measurements. - The Associative Property is used as a strategy to multiply single digit factors with multiples of ten. |
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| whole, fraction, equal parts, partition, fractional parts, halves, thirds, fourths, quarters, sixths, eighths, numerator, denominator, unit fraction, non-unit fraction, same, different, size, equivalent fractions, subtract a group, add a group, helper facts, doubling, factors, product, missing factor, decompose, multiples, even, odd, pattern, near squares, break-apart strategy Bold: Listed in teacher's EDM4 edition Normal Font: not listed in teacher’s edition as a vocabulary word but will be helpful for students in explanations |
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| The following lesson plan sequence is obtained from Everyday Mathematics 4. Each lesson is aligned with a learning objective to inform the teachers on what students should be able to at the end of the lesson. The student objective informs the students of their learning goals for the day and it should be reviewed before, during and at the end of the lesson. Each lesson includes a mathematics task that should be implemented to meet the learning objectives. Teachers can select from the practice opportunities to reinforce the learning goals of the day. |
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| The following language supports are for English Language Learners but could also be used to support any struggling learner in mathematics. The strategies are obtained from the SIOP model. The language objectives will support students' academic language development. The sentence stems and starters provides the support many students need to be able to participate in discussions and writing about mathematics. |
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