Grouping numbers to add
CONCEPTUALUnderstand and apply the associative property of addition: when adding three numbers, any two can be added first
Mastery Evidence
- Solve 2 + 6 + 4 by first adding 6 + 4 = 10, then 2 + 10 = 12
- Explain that grouping addends differently gives the same total
- Choose which two numbers to add first to make the calculation easier
Assessment Prompt
“If [child] needs to add 3 + 7 + 6, can they spot that adding 3 and 7 first (to make 10) is easier — rather than always working left to right?”
Curriculum Standards1 alignment
1.OA.3Common Core State Standards for MathematicsApply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
Prerequisites2
- Addition as combining or putting together twohardAges 4—6
- Addition in any orderhardAges 6—7
Show full prerequisite tree
- Addition as combining or putting together two hard
Associativity requires understanding addition as combining
- 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'
- Addition in any order hard
Associative property builds on commutative — both involve rearranging addends
- Addition as combining or putting together two hard
Understanding commutativity of addition 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'
Unlocks1
- Adding Three Small NumbershardAges 6—7