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Mathematical Problem Solving by Flexible Resilient
MathematiciansPresented by Tracy Ortiz, Jamie Reichelt, and Jenna Stenclik
Addition and Subtraction Strategies in First Grade
How to Become a More Efficient Mathematician
11stst Grade Expectations Grade Expectations Master a number of different addition/subtraction strategies.
Choose the strategies that work best for him/her and for the particular problem.
Be flexible with strategies and choose ones that are efficient.
Check work with another strategy.
Full ModelFull Model
Counting objects, counting on fingers, drawing a picture
Show your work by Drawing all for addition
Taking away objects, taking away fingers, crossing off in a picture
Show your work by Drawing all and crossing off for subtraction
Prompt: How can you use a picture to solve this problem?
Prompt: How can you use a number line Prompt: How can you use a number line
and/or counting to solve this problem?and/or counting to solve this problem?
3 + 8 = ___
8 – 2 = ___
Counting On/Counting Counting On/Counting BackBack
Adding and subtracting are like counting up and back
Start with the larger number and count on or back (“hop”/”jump” forward or back)
Efficient strategy for solving single-digit addition and subtraction problems
Show your work with a number line or drawing a picture of the number in your head and dots
Using Facts We Know (Fluency)Using Facts We Know (Fluency)
Combinations of 10
6 + 3 + 4 = ____ I know 6 + 4 = 10 and 10 + 3 = 13
Doubles and Near Doubles
8 + 7 = _____ I know 7 + 7 = 14, so one more is 15
Fact Families – using what we know about addition to help with subtraction
10 – 7 = ____ I know 7 + 3 = 10, so 10 – 7 = 3
Fluency is so important because it is the foundation to solve more difficult problems.
Show your work with words and equations.
PromptPrompt: How can you break a number : How can you break a number
into helpful parts to solve this problem?into helpful parts to solve this problem?
9 + 7 = ___
Keep One/Break OneKeep One/Break One Importance of flexibility with numbers, knowing how to break numbers
apart in multiple ways.
Show your work with number bonds and/or equations.
Break one number into two parts so that you can make a landmark number
(e.g., 10 or a multiple of 10)
9 + 7 = ____
18 – 9 = ____
36 + 8 = ____
PromptPrompt: How can you use what you : How can you use what you
know about 10s and 1s to solve this know about 10s and 1s to solve this
problem?problem?
36 + 22 = ___
Using Place ValueUsing Place Value
Base 10 Model: Using or drawing base 10 blocks
Expanded Form: Breaking numbers into 10s &1s
30 + 6
20 + 2
50 + 8 = 58
Keep One/Break One: Adding multiples of 10 first
36 + 20 = 56 56 + 2 = 58
Show your work with base 10 drawings and/or equations
36 + 22 = ____
1st Grade Word Problem Comprehension
Do NowDo NowSolve the Following Problem: Solve the Following Problem:
John has 8 books. He has a green basket and a blue basket. How many books can he put in each basket?
Solve the Problem by Answering the Following:
Draw a picture to show what is happening in the problem
Write an equation to represent what is happening in the story.
What kind of problem is this?
How Did You How Did You Solve this Problem? Solve this Problem?
What did you envision?
What did you draw?
How did you solve this word problem?
What type of word problem is this?
What is Word Problem What is Word Problem Comprehension?Comprehension?
Think about the word problem like a story
You are a math detective, use the clues to help you solve the problem
Complete the Word Problem Complete the Word Problem &&
Think About the Following: Think About the Following:
Word Problem TypesWord Problem Types
How to Help Your ChildHow to Help Your Child Help them envision by having them sketch
Use prompts to help them think about the word problem like a story
Encourage them to THINK about the problem, before they attempt to solve it
Have your child explain WHY they solved the problem they did
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