Begin with the End in Mind: By the end of this unit, students should be able to respond to the following prompts: |
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Who is correct? Prove it by using an area model, number line, and a written explanation. |
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Common Core Clusters and Standards |
Standards for Mathematical Practic |
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Use the four operations with whole numbers to solve problems. 4.OA.1 4.OA.2 4.OA.3
Gain familiarity with factors and multiples. 4.OA.4 |
During this unit, focus on MP2 (Reason abstractly and quantitatively). Facilitate During this unit, focus on MP7 (Look for and make use of structure). Once students |
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Take Note! Notes about each Investigation |
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1 |
Rectangualr arrays are used as tools to highlight important relationships and properties as well as to solve problems. Session 1.3 introduces students to prime and composite numbers. Look for multiple opportunities to ask students whether or not a number from 1-100 is prime or composite and explain how they know. Common Core Snap-In provides Session 1.6A which introduces multiplicative comparison situations (standards 4.OA.1 and 4.OA.2). Further development of these standards is needed as students begin translating comparative situations into equations with unknowns. |
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2 |
Quick Images will be introduced during this investigation. Explicit use of “prime and composite” is encouraged while attending to precision. |
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3 |
Investigation 3 extends standard 4.OA.4 by using factors of 100 to find factors of multiples of 100 (200, 300…) and by finding factors of related numbers (introduction to concept of common multiples). Additional experiences for proving that factors of one number always being factors of multiples of that number are provided. |
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The Language of Mathematics - Words students should use precisely during mathematical conversations. |
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Factor, unknown, dimension, array, product, prime, multiple, composite |
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Routine |
Corresponding Common Core State Standards and Notes |
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Today’s Number |
4.NBT.1 and 4. NBT.2 Students work within the operations of addition and subtraction to generate equivalent expressions that yield a given number. Be sure to show equivalency between expressions and have students precisely explain their strategies. |
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Counting Around the Class |
4.OA.3, 4.OA.4, and 4.OA.5 Students find the multiples of a given number (factor) while skip counting (numerical pattern). Have students occasionally provide equations to model stated multiples, e.g., “What equation represents what the ninth person said while counting by 4’s? (9 groups of 4 is 36 or 9 x 4 = 36). This will help them understand the relationship between skip counting and multiplication. |
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Quick Images |
4.OA.5 Subitizing (quick images) promotes organizing and analyzing visual images, increases computational fluency, and allows students to model with mathematics by generating equivalent expressions (equations). |
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When students struggle, have them... |
When students clearly understand, have them… |
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- Have students use manipulatives/tools like colored tiles, snap cubes, and grid paper to build and/or replicate arrays (concrete models). Also, provide real-life examples. - Work Work with smaller numbers while representing multiplication situations. |
-Encourage students to use the distributive property to multiplication expressions. |
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Technology Connections |
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Investigation 1 Smart Board Lesson (These are updated now on the new page) Investigation 2 Smart Board Lesson Investigation 3 Smart Board Lesson |
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Professional Learning Opportunities |
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Why is it important for students to develop strong visual images of multiplication? Read “Images of Multiplication,” pp. 115-116. How does using arrays to represent multiplication increase multiplicative understanding? Read “Representing Multiplication with Arrays,” pp. 117-119. How can I help my students learn their multiplication combinations fluently? Read “Learning and Assessing Multiplication Combinations,” pp. 120-122. |
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End of Unit 1 Assessment Rubric 4th Grade Vocabulary List in English and Spanish Investigations Vocabulary Investigations Unit Vocabulary 3-5 Literature List Extension Projects for Investigations Literature for Unit 1: One Hundred Hungry Ants Each Orange Had Eight Slices What Comes in 2’s, 3’s, and 4’s Anno’s Mysterious Counting Jar. Two Ways to Count to Ten
Illuminations: All About Multiplication Activities -Representing Multiplicative Comparison Problems -Multiplicative Comparison Problems
Games *Remember to upload files to share with others, or locate files to use, on the wiki. Be sure to join discussion posts with other colleagues to ask questions, answer questions, and discuss math. |
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