Addition in any order
CONCEPTUALUnderstand and apply the commutative property of addition: addends can be added in any order
Mastery Evidence
- Explain that 3 + 8 gives the same answer as 8 + 3
- Use commutativity to choose the larger number to count on from
- Demonstrate that subtraction is not commutative (5 − 3 ≠ 3 − 5)
Assessment Prompt
“Does [child] know that 6 + 4 gives the same answer as 4 + 6, so they can always choose whichever order makes the adding easier?”
Curriculum Standards2 alignments
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.)
Maths/Y2/AS/8The national curriculum in EnglandShow that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot.
Prerequisites1
- Addition as combining or putting together twohardAges 4—6
Show full prerequisite tree
- 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'
Unlocks3
- Shape patternssoftAges 6—7
- Explaining Mathematical ReasoningsoftAges 6—7
- Grouping numbers to addhardAges 6—7