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Lesson Plan

Mary's Flower Garden: Trajectory of Understanding

teaches Common Core State Standards CCSS.Math.Practice.MP2
teaches Common Core State Standards CCSS.Math.Practice.MP7
teaches Common Core State Standards CCSS.Math.Content.3.OA.B.5

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Students will understand that the array can be decomposed in a variety of ways, and the number of flowers can be represented using combinations of multiplication and addition. Students are provided a visual to begin with, and are asked to divide it up in different ways and write expressions to represent how they divided up the arrays The suggested public discussion of student work shows a trajectory of understanding. Discussing this work publicly is important because students are just beginning to use operations together and grouping symbols such as parentheses. It is also important for students to connect the numerical expressions to a visual representation. Three pieces of work are shown, beginning with a response that shows a workable idea, but incorrect notation, as the student represents two groups of 4 as 4 x 4. This is followed by work that shows 8 decomposed into 5 and 3, as well as the use of addition and multiplication together, but is missing grouping symbols for 3+5. Finally, a correct decomposition and expression is shown. The trajectory of understanding builds from a correct idea with incorrect notation through more formal and correct notation.
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