Counting on: Starting with the larger number and counting up
- Start with the larger number (8)
- Count up 5 more: 9, 10, 11, 12, 13
- The answer is 13
We start with 8 (the larger number)
Count 5 more: 9, 10, 11, 12, 13
The last number counted is the answer
8 + 5 = 13
8 + 5 = 13
• Counting on strategy: Start with the larger number
• Sequential counting: Count each number in sequence
• One-to-one correspondence: Each count represents one added
Making ten: Breaking apart one number to make 10 with the other
9 is close to 10, needing 1 more
4 = 1 + 3 (so we can make 10 with 9)
(9 + 1) + 3 = 10 + 3 = 13
10 + 3 = 13
9 + 4 = 13
• Making ten strategy: Use 10 as a benchmark
• Decomposition: Break apart numbers strategically
• Associative property: Group numbers differently
Doubles plus one: Using a doubles fact and adding one more
6 + 7 is close to 6 + 6
6 + 6 = 12
Since 7 is one more than 6, add 1 to the double
12 + 1 = 13
6 + 7 = 13
• Doubles plus one strategy: Use known doubles facts
• Near doubles: Numbers that differ by 1
• Pattern recognition: See relationships between numbers
Counting back: Starting with the larger number and counting down
We start with 12 (the larger number)
Count 5 back: 11, 10, 9, 8, 7
The last number counted is the answer
12 - 5 = 7
12 - 5 = 7
• Counting back strategy: Start with the larger number
• Sequential counting: Count each number in sequence
• Subtraction: Taking away reduces the total
Think addition: Using addition facts to solve subtraction problems
What number added to 8 equals 15?
8 + 7 = 15
15 - 8 = 7
15 - 8 = 7
15 - 8 = 7
• Think addition strategy: Use addition to solve subtraction
• Inverse operations: Addition and subtraction are opposites
• Fact families: Related addition and subtraction facts
Subtraction with regrouping: Breaking apart numbers to make subtraction easier
13 = 10 + 3
10 - 6 = 4
4 + 3 = 7
13 - 6 = 7
13 - 6 = 7
• Regrouping strategy: Break numbers into helpful parts
• Subtract from 10: Use 10 as a benchmark
• Decomposition: Break apart numbers strategically
Within 20 Practice
Addition & Subtraction Strategies
Counting On: Start at 8, count 5 more
Counting Back: Start at 12, count 5 back
Practice Makes Perfect!
This section provides a comprehensive overview of addition and subtraction within 20, including definitions, methods, strategies, and key concepts for 1st grade students.
Addition: Combining numbers to find a total or sum.
Subtraction: Taking away one number from another to find the difference.
Within 20: Problems where the answer is 20 or less.
Counting On: Starting with the larger number and counting up.
• Addition increases the total
• Subtraction decreases the total
• The sum of two numbers within 20 will never exceed 20
• Order doesn't matter in addition (commutative property)
Counting On: Start with the larger number and count up
Making Ten: Break apart numbers to make 10 with one addend
Doubles Plus One: Use known doubles facts
Number Line: Visual representation of addition
Counting Back: Start with the larger number and count down
Think Addition: Use addition facts to solve subtraction
Fact Families: Use related addition and subtraction facts
Decomposition: Break apart numbers strategically
Addition: 8 + 5 = 13 (count on: 8, 9, 10, 11, 12, 13)
Subtraction: 13 - 5 = 8 (count back: 13, 12, 11, 10, 9, 8)
Making Ten: 9 + 4 = 9 + 1 + 3 = 10 + 3 = 13
Think Addition: 15 - 8 = ? → 8 + ? = 15 → answer is 7
• Start with the larger number when counting on
• Practice doubles facts regularly (they help with near doubles)
• Use 10 as a benchmark number for easier addition
• Always check your answer by using the opposite operation
Questions & Answers
Question: Why do we learn to "make 10"? Isn't it easier to just count everything?
Answer: Great question! Making 10 is actually much faster and easier once you get good at it!
Let's compare:
For 9 + 4:
- Counting all: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 (13 counts!)
- Making 10: 9 + 1 = 10, then 10 + 3 = 13 (just 2 steps!)
Making 10 is like having a shortcut. Also, knowing 10 facts really well helps you with bigger numbers later, like 19 + 4 or 29 + 4.
Think of 10 as a "friendly number" that makes addition easier. Once you practice enough, making 10 becomes automatic and much faster than counting everything!
It's like learning a secret code that makes math faster!
Question: My child is still counting on their fingers for addition and subtraction within 20. Should I be concerned, and how can I help them move beyond finger counting?
Answer: Finger counting is completely normal and appropriate for 1st graders! Don't worry - it shows your child is developing number sense.
Here are strategies to help transition from finger counting:
- Use visual aids: Number lines, ten frames, or dot cards
- Practice mental math: Start with very easy problems and gradually increase
- Teach efficient strategies: Counting on from the larger number, making ten
- Build fluency: Regular practice with doubles and near doubles
- Gradual reduction: Encourage "just trying it in your head" for easier problems
Focus on building number relationships and strategies rather than rushing to eliminate finger counting. The mental strategies will develop naturally with practice and exposure to different approaches.
It typically takes several months of consistent practice to reduce reliance on finger counting.
Question: How do I know when to add and when to subtract? Sometimes I mix them up!
Answer: Great question! Here's how to tell:
Addition words: "more," "added," "total," "altogether," "in all," "combined"
Subtraction words: "left," "remaining," "takes away," "eats," "loses," "gives"
Think about what's happening:
- Addition: Something is being added or joined together
- Subtraction: Something is being taken away or separated
For example:
- "Sarah has 8 apples and gets 4 more" → ADDITION (she has MORE)
- "Tom had 12 cookies and ate 5" → SUBTRACTION (he has FEWER)
When in doubt, draw a picture to help visualize what's happening!