1. Exploring Addition and Subtraction Situations Math Alliance March 8 & 9, 2010

2. Thinking About Addition and Subtraction The most familiar way to think of addition and subtraction are as combining and taking away. (Beckmann, 2005)

3. WALT We are learning to… –Broaden our understanding of addition and subtraction. –Explore various kinds of situations involving addition and subtraction. We know we will be successful when… –Identify the word problem type for a given word problem, and pose word problems that naturally match specific equations.

4. Exploring Addition and Subtraction Situations Work as a team. Make sure to follow the word problem on the card as it is stated. Person 1: Pick a card and read the problem situation out loud to the group. Person 2: Act out the situation with counters in a manner that naturally fits the story. Person 3: Write the number sentence that reflects and matches the situation.

5. Word Problem Structures –Add to (Join) –Part-Part-Whole (Put Together/Take Apart) –Take Away (Take From, Separate) –Compare

6. Identifying Story Structures Make 4 sticky notes with these labels: –Add to –Part-Part-Whole –Take Away –Compare Sort the problems you just worked by the problem type.

7. Representing Word Problem Structures 9 ? 3 3 6 ? One set of objects being combined or separated. Two sets of objects being compared.

8. Match Diagrams to Word Problem Structures Pick a diagram. Study it quietly on your own. Decide on which story it matches. Describe why you think the diagram matches that particular word problem. Take turns completing the activity.

9. Debrief Which of these problems do you think might be hardest for young children? Why?

10. Basic Addition & Subtraction Equations Addition A + B = CC = A + B Subtraction D – E = FF = D – E In what way does this become problematic when one term is missing?

11. Add to or Join Clare had 3 bears. After she got some more bears, Clare had 9 bears. How many bears did Clare get? 3 + ? = 9 Clare had some bears. After she got 3 more bears from a friend, Clare had 9 bears. How many bears did Clare have to begin with? ? + 3 = 9

12. Take Away or Separate Clare had 9 bears. After she gave away some bears to her brother, Clare still had 3 bears. How many bears did Clare give away? 9 – ? = 3 Clare had some bears. After she gave away 3 bears to her cousin, she had 6 bears left. How many bears did Clare have to begin with? ? – 3 = 6

13. Part-Part-Whole Two distinct parts that make a whole; no action. Clare has some red bears and some blue bears. She has 3 blue bears. All together, Clare has 9 bears, and all of them are either red or blue. How many red bears does Clare have? ? + 3 = 9 Clare has some red bears and some blue bears. She has 3 red bears and she has 6 blue bears. How many bears does Clare have? 3 + 6 = ?

14. Compare Problems A comparison of two quantities or sets. Clare has 3 red bears. She also has 6 more blue bears than red bears. How many blue bears does Clare have? 3+6 = ? Clare has 9 red bears and 3 blue bears. How many more red bears does Clare have than blue bears? 3 + ? = 9 or 9 - 3 = ?

15. Addition and Subtraction Relationships The relationship between addition and subtraction gives rise to problems that can be solved by addition but are not “add to” and problems that can be solved by subtraction, but are not “take away”. (Beckmann, 2005)

16. Thinking About Solution Approaches 6 + 3 = ? – 6 = 9 Can be solved by adding 6 + ? = 9? + 6 = 9 9 – 6 = ?9 – ? = 6 Can be solved by subtracting

17. Homework (a) Read “Math for Elementary Teachers” text, pages 125-130. (b) Problems for Section 4.1, complete 1-5. (c) Reflect in writing to: What observations can you make as you compare the diagrams to the various word problem types? What connections can you make from this study of word problems to your work with students?