CCSS.Math.Content.HSN-VM.C.7
The Standard
(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
Common Core State Standards for Mathematics · Vector and Matrix Quantities
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students multiply each entry in a matrix by the same number. They connect that operation to scaling quantities, such as prices, payoffs, or measurements.
What Mastery Looks Like
- Students correctly multiply each matrix entry by positive, negative, fractional, or decimal scalars. They keep the matrix dimensions unchanged and interpret the result in context.
Common Misconceptions
- Students may multiply only one row or column instead of every entry. They may add the scalar, miss negative signs, or change the matrix dimensions.
How to Assess It
- Give students the matrix [[3, -2], [0, 5]] and scalar -4. Ask them to find the product and describe what happens to the dimensions.
Lesson moves
Ways to Teach It
Give students a 2 by 3 matrix on six tiles; draw a scalar card, then replace each tile with the correct product.
Prompt: A store doubles every price in a matrix; explain why multiplying only one row is wrong.
Play Matrix Match: students pair scalar and matrix cards with product-matrix cards, then justify one match to a partner.
Use a matrix of hourly pay for three jobs and two shifts, then calculate all rates after an increase by a factor of 1.5.
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Printable HSN-VM.C.7 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSN-VM.C.7, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.7.NS.A.2c
Scalar matrix multiplication applies rational-number multiplication to each entry, so sign, fraction, and operation-property fluency supports the matrix work.
- CCSS.Math.Content.HSN-VM.C.6
Understanding matrices as arrays of quantities supports interpreting scalar multiplication as scaling every represented data value.
- CCSS.Math.Content.HSN-VM.B.5a
Multiplying each vector component by a scalar transfers directly to multiplying every matrix entry by that scalar.
What This Unlocks
Mastery here sets students up for these next.
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