Addition and subtraction strategies
PROCEDURALUse counting on and counting back as strategies for addition and subtraction
Mastery Evidence
- Add 8 + 3 by starting at 8 and counting on 3 (9, 10, 11)
- Subtract 12 − 3 by counting back 3 from 12 (11, 10, 9)
- Explain that counting on is a way to add
Assessment Prompt
“If [child] needs to work out '8 + 5', can they start from 8 and count up five more — rather than starting from 1 every time?”
Curriculum Standards1 alignment
1.OA.5Common Core State Standards for MathematicsRelate counting to addition and subtraction (e.g., by counting on 2 to add 2).
Prerequisites3
- Addition as combining or putting together twohardAges 4—6
- One More Each TimehardAges 4—6
- Subtraction as taking away or separatinghardAges 4—6
Show full prerequisite tree
- Addition as combining or putting together two hard
Counting on as an addition strategy requires understanding addition
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- One More Each Time hard
Counting on/back relies on understanding that each successive number is one more/less
- How Many in Total? hard
Understanding 'one more/one less' requires understanding that each number represents a quantity (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Subtraction as taking away or separating hard
Counting back as a subtraction strategy requires understanding subtraction
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
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