CCSS.Math.Content.HSN-VM.C.9
The Standard
(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
Common Core State Standards for Mathematics · Vector and Matrix Quantities
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students compute products of square matrices in different orders and compare the results. They verify with examples that regrouping three factors or distributing across a sum preserves the result.
What Mastery Looks Like
- Given compatible matrices, students accurately find AB and BA and explain why they may differ. They can verify regrouping and distribution using correct matrix calculations.
Common Misconceptions
- Students often treat matrices like ordinary numbers and assume AB equals BA. They may confuse changing order with changing grouping, or multiply matching entries instead of using row-by-column products.
How to Assess It
- Exit ticket: Let A = [[1,1],[0,1]] and B = [[1,0],[1,1]]. Find AB and BA, then explain what the results show about factor order.
Lesson moves
Ways to Teach It
On a coordinate grid, use tracing paper to apply a stretch and a rotation in both orders, then record each resulting image.
Calculate AB and BA for one pair, then write two sentences explaining why equal dimensions do not guarantee equal products.
Match cards showing matrix expressions, expanded products, and results for associative and distributive examples, then justify every match to a partner.
Plot a four-point logo, then use transformation matrices to compare resizing before rotation with rotation before resizing.
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Printable HSN-VM.C.9 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSN-VM.C.9, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
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Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSN-VM.C.8
Students need matrix addition and multiplication to test noncommutativity and verify associative and distributive properties for square matrices.
- CCSS.Math.Content.7.EE.A.1
Using associative and distributive properties with expressions supports recognizing which operation properties matrix multiplication keeps or loses.
What This Unlocks
Mastery here sets students up for these next.
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Related Standards
- CCSS.Math.Content.HSN-VM.C.7
(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
- CCSS.Math.Content.7.NS.A.2a
Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, par...
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