Students will work with a partner to write, solve, check, and animate a …

Students will work with a partner to write, solve, check, and animate a division story problem based on a division expression using a sharing model.

Topic C introduces formal addition concepts including writing and solving expressions and …

Topic C introduces formal addition concepts including writing and solving expressions and equations. The first three lessons ask students to represent addition story problems involving decomposition and composition, modeled by A + B = C and C = A + B. In these first formal addition lessons the stories are told with no unknown. “There are 7 apples in the bowl. 5 of them are red and 2 of them are green.” Students write addition sentences and identify the referent of each number within the problem. Lessons 13–15 work with 6, 7, and 8 respectively, representing such addition stories with pictures, numbers, and equations. In Lesson 16, students solve add to with result unknown (A + B = ___) word problems within 8. “There were 5 birds in the tree. 3 more birds flew to the tree. How many birds are in the tree now?” Students learn to put a box around the equation’s unknown. Lesson 17 teaches put together total unknown (also A + B = ___) word problems. On the surface these problems appear similar those of Lesson 16, but lack the embedded action of the previous problems. Instead, they focus on a set of objects and part–whole relationships. “There are 4 red toy cars and 3 blue toy cars on the table. How many toy cars are on the table?” Lesson 18 deals with the last type of addition situation in kindergarten, both addends unknown (C = ___+___). Note that this take apart situation is modeled with an addition equation. Students are given a total and are asked to find a number pair in the context of an addition story. “There were 8 toy cars. Some are on a shelf and the rest are in a toy box. Write an addition sentence to show how many could be in each place.” For examples of all problem types, refer to the Operations and Algebraic Thinking progression document, page 9.

Topic D introduces formal subtraction concepts including writing and solving expressions and …

Topic D introduces formal subtraction concepts including writing and solving expressions and equations. Lesson 19 begins at the concrete level with students acting out take away stories and working at the pictorial level crossing off to see what remains. In Lesson 20, the concrete objects and pictorial representations are tied to or matched to the representative subtraction expression or equation using the minus sign with no unknown. As in Topic C, this progression helps students move from concrete processes to reasoning abstractly and quantitatively (MP.2). In Lesson 21, students solve subtraction story problems using concrete and pictorial representations and write the corresponding equation. As with addition, it is important that students understand what each numeral in the equation represents from the story situation. Lessons 22–24 focus on decompositions of 6, 7, and 8, which are recorded as equations. These equations are described in the progressions as take from with result unknown (C – B = ___) situations. These three lessons explore the decompositions of 6, 7, and 8 by breaking off a part, hiding a part, and crossing off a part. “There were 7 bears sleeping in a cave. Four bears left to go fishing. How many bears are still in the cave?”

Topic G provides additional practice with formal subtraction concepts, including writing and …

Topic G provides additional practice with formal subtraction concepts, including writing and solving number sentences with totals of 9 or 10. Lesson 33 moves quickly through concrete and pictorial representations of subtraction with students representing take from equations (C − B = A), with no unknown for totals to 10. “There were 10 cars in the parking lot. Two of them drove away. Now there are 8 cars left in the parking lot.” In Lesson 34, students solve subtraction story problems by breaking off, crossing out, and hiding a part and show their strategies with drawings and number sentences (MP.5). “I have 9 pencils. I’m going to hide 3 pencils in a box. How many pencils are not in the box?” Lessons 35–36 focus on decompositions of 9 and 10 using 5-groups, which are recorded as number sentences (K.OA.3). These decompositions differ from those in Topic F in that they are represented as subtraction number sentences (C – B = A) instead of addition sentences (C = __ + __ ). Students continue to focus on the grade level fluency goal during Fluency Practice, improving the speed and accuracy with which they can add and subtract numbers to 5 (K.OA.5).

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