1. Using Addition to Subtract
Unpacking Unknown Addend Situations
Common Core Leadership in Mathematics (CCLM) University of Wisconsin-Milwaukee
Wednesday June 22, 2011
Melissa Hedges & DeAnn Huinker

2. This Morning’s Motto
“Learning is a messy business, and constructing understanding is hard work.”
-Fosnot & Dolk, Young Mathematicians At Work p.38.

3. Learning Intention and Success Criteria
We are learning to…
Recognize the role unknown addend situations and equations play in developing fluency with single-digit problems.
Understand “think addition to subtract” and explore how to build that understanding in students.
We will be successful when we...
Understand how to use addition and subtraction word problems, situation equations, and solution equations to support students’ ability to reason fluently.

4. Unknown Addend Problems
Read
K.OA.2, K.OA.4, 1.OA.1, 1.OA.4, 2.OA.1
Highlight essential ideas in each.
Discuss the progression from Kindergarten to grade 2 in developing the idea of an unknown addend.
All come up one by one

5. Food for thought….
Learning to think of and solve subtractions as unknown addend problems makes subtraction as easy as addition (or even easier), and it emphasizes the relationship between addition and subtraction.
K-5 OA Progressions document, p. 15

6. Scan: Handout on “Addition & Subtraction Problem Situations.”
(Table 1 revised)
Which are the easier problem situations to solve? Why?
Which problem situations prompt Level 2 and Level 3 reasoning?

7. Addition and Subtraction Problem Situations
Result Unknown
Change Unknown
Start Unknown
Add To
(join)
Eight frogs sat on the grass. Three frogs jumped out of the pond and joined them on the grass. How many frogs are on the grass now?
8 + 3 = ☐
Eight frogs were sitting on the grass. Some other frogs jumped over there and joined them. Then there were eleven frogs on the grass. How many frogs jumped over to join them?
8 + ☐ = 11
Some frogs were sitting on the grass. Three other frogs jumped over there to join them. Then there were eleven frogs. How many frogs were on the grass before those three joined them?
☐ + 3 = 11
Take From
(separate)
Eleven grapes were in a bowl. I ate eight of the grapes. How many grapes are in the bowl now?
11 – 8 = ☐
Eleven grapes were in a bowl. I ate some of the grapes. Then there were three grapes remaining in the bowl. How many grapes did I eat?
11 – ☐ = 3
A bowl held a bunch of grapes. I ate eight grapes. Then there were three grapes remaining in the bowl. How many grapes were in the bowl before I ate some?
☐ – 8 = 3
Total Unknown
Addend Unknown1
Both Addends Unknown2
Put Together or
Take Apart
The vase held three red flowers and eight yellow flowers. How many flowers were in the vase?
3 + 8 = ☐
Eleven flowers are in the vase. Eight are red flowers and the rest are yellow. How many flowers are yellow?
8 + ☐ = 11
11 – 8 = ☐
Grandma has eleven flowers in a vase. Some of the flowers are red and some are yellow. How many flowers of each color might she have?
11 = ☐ + ¯
Difference Unknown
Bigger Unknown
Smaller Unknown
Compare
“How many more?” version:
Nakeia has eight apps on her iPhone. and Justin has eleven apps on his. How many more apps does Justin have than Nakeia?
“How many fewer?” version:
Nakeia has eight apps on her iPhone. and Justin has eleven apps on his. How many fewer apps does Nakeia have than Justin?
8 + ☐ = 11
11 – 8 = ☐
“More” version with “more”:
Justin has three more apps on his iPhone than Nakeia has on hers. Nakeia has eight apps. How many apps does Justin have?
“Fewer” version:
Nakeia has three fewer apps on her iPhone than Justin has on his iPhone. Nakeia has eight apps. How many apps does Justin have?
8 + 3 = ☐
“More” version:
Justin has three more apps on his iPhone than Nakeia has on her iPhone. Justin has eleven apps. How many apps does Nakeia have?
Nakeia has 3 fewer apps on her iPhone than Justin has on his iPhone. Justin has eleven apps. How many apps does Nakeia have?
☐ + 3 = 11
11 – 3 = ☐

8. Situation vs Solution Equations
Read p OA Progressions document:
“Representing and solving the subtypes for all unknowns in all three types.”
Discuss the differences between a situation equation and a solution equation.
Why is it important as an algebraic building block to have students represent word problems with situation equations?

9. Two types of equations Situation Equation:
Matches the structure of the story.
Solution Equation:
Equation is re-represented (re-written) into an equation that promotes Level 2 or Level 3 method.
Turn and Talk: What does this mean?
Level 2 Counting on
Level 3 Convert to an easier equivalent problem – Think addition

10. Practicing reasoning…
Facilitators:
Pull out a word problem card.
Show and read the card to your group.
Individually each person:
Identify the problem type.
Write a situation equation for the word problem, if needed re-represent it as a solution equation.
Jot down student reasoning at Level 2 or Level 3 and show “using objects, drawings, or equations.”
As a table group:
Share your equations.
Talk through the student reasoning.

11. Pathways… Find K-8 Domains section in your binder.
Show how these standards are connected and build across grades by drawing lines and arrows.
K.OA: 2, 3 & 4
1.OA: 1, 3, 4 & 6
2.OA: 1 & 2

12. Learning Intention and Success Criteria
We are learning to…
Recognize the role unknown addend situations and equations play in developing fluency with single-digit problems.
Understand “think addition to subtract” and explore how to build that understanding in students.
We will be successful when we...
Understand how to use addition and subtraction word problems, situation equations, and solution equations to support students’ ability to reason fluently.