# Decomposing Numbers (Operations and Algebraic Thinking)

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1 Decomposing Numbers (Operations and Algebraic Thinking) Kindergarten Formative Assessment Lesson Designed and revised by Kentucky Department of Education Mathematics Specialists Field-tested by Kentucky Mathematics Leadership Network Teachers Created for the sole purpose of assisting teachers as they develop student understanding of Kentucky s Core Academic Standard through the use of highly effective teaching and learning. Not intended for sale.

4 will be of help to the majority of students. These can be written on the board at the end of the lesson before students revisit initial task. The solution to all these difficulties is not to teach one particular way of counting or adding, but to help students find a variety of ways that work in different situations and make sense to them. Below is a list of common issues and questions/prompts that may be written on individual initial tasks or during the collaborative activity to help students clarify and extend their thinking. Common Issues: Suggested questions and prompts: Students may not choose cards as equal because they are What does it mean to be equal? in a different order. Is this (three fingers and two fingers) the same as this (two fingers and three fingers)? Why or why not? Students may choose card as equal that has same numbers. What do the numbers mean when we put them together? Can you show how many altogether? Students may have incorrect answers due to miscount. How did you decide how many there were? Show me how you counted. Do you get the same number every time you count? Students may think some cards do not have matches because of the structure of the problem with the sum What does an equal sign mean? Often times student view the equal sign as an indication of an listed first. E.g. 9 = answer. It needs to be viewed as both sides representing the same amount. Use a balance scale and have student build problem with linking cubes, crayons, etc. Students think that three hands in the finger pattern cards mean there are three addends. What is another way to say 5 and 1? How many are above the line? How many are below the line? 4

6 This task is designed for students to apply mental strategies they have been developing during the unit of instruction. Manipulatives should only be considered for students who have exhausted all other strategies. Placing Card Set B (Stars) As students finish with matching card set A, have students explain their thinking before handing out card set B. These provide students with a different way of interpreting the equations. Do not collect card set A. An important part of this task is for students to make connections between different representations of equations. As you monitor the work, listen to the discussion and help students to look for patterns and generalizations. Placing Card Set C (Finger Cards) As students finish matching card set B, have students explain their thinking before handing out card set C. Continue to monitor work and listen to discussion. Do not collect any of the card sets, allow students to continue to add on to previously completed work. Question and prompt students to look for differences and similarities as they work. Placing Card Set D (Irregular Patterns) As students finish matching card set C, have students explain their thinking before handing out card set D. Continue to monitor work and listen to discussion. Card Set D contains three additional cards to expose student misconception that just matching numbers always yields equality. Do not collect any of the card sets, allow students to continue to add on to previously completed work. Question and prompt students to look for differences and similarities as they work. Extension activities Two additional card sets are included to extend student work. Card Set E and. Continue work in same manner as previous card sets. Plenary whole-class discussion (10 minutes) Call on students or groups to explain why various cards are equal or not equal and the strategies used to decide. Have them explain why some cards match the equations and some don t. You might have students discuss other representations that would be equal for each equation and how they know they are equal. Perhaps give each student a mini-whiteboard, pen, and eraser and have them draw a picture or write an expression or equation that is equal. Conclude the lesson by discussing and generalizing what has been learned. The generalization involves first extending what has been learned to new examples, and then examining some of the conclusions the students come up with. Improving individual solutions to the assessment task (10 minutes) 6

7 Return to the students their original assessment, What s Equal?, as well as a second blank copy of the task. Look at your original responses and think about what you have learned during this lesson. Using what you have learned, try to improve your work. If you have not added questions to individual pieces of work then write your list of questions on the board. Students should select from this list only the questions appropriate to their own work. (With kindergarten, you may only focus on the questions students really seemed to need and state these out loud and ask them again as you move around the room or work with a small group at a time.) 7

8 What s Equal? Formative Assessment Lesson Alpha Revised 4/2012 Circle all the cards that are equal to the top card in each box. NAME =8 2+4=6 6= = =4+5 7= =9 4+3=7 7+3=4 Finger pattern art work by Steve Peck 8

9 Card Set A 6+3=9 7+1=8 5+2=7 5=3+2 3=2+1 10=6+4 9

10 Card Set B Card Set C Finger pattern art work by Steve Peck 10

11 Card Set D Card Set E 11

12 2+3=5 2+1=3 6+4=10 9=3+6 8=7+1 7=2+5 2=3+5 7=1+8 5=2+7 12

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