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
What this standard means
Students need to multiply every entry in a matrix by the same number. They should know that the matrix keeps the same size, but each value changes by the scale factor. They also need to connect this to contexts, such as doubling scores, cutting costs in half, or applying a fee increase.
Mastery looks like clean, accurate scalar multiplication with positives, negatives, fractions, and decimals. Students can explain what the new matrix means in context. Common mistakes include multiplying only one row or column, changing the dimensions, dropping negative signs, or treating scalar multiplication like matrix multiplication.
Ways to teach it
- Hands-on activity: Give pairs a 3 by 3 price matrix and sale cards like half off, triple, and 1.08 tax to compute new matrices.
- Discussion prompt: Ask, “If every payoff in this game doubles, what changes in the matrix and what stays the same?”
- Quick assessment: Display a 2 by 3 matrix and ask students to multiply it by -4 on mini whiteboards in two minutes.
- Real-world connection: Use a school concession stand cost matrix and have students apply a 25 percent price increase to every item.
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Related standards
- CCSS.Math.Content.HSN-VM.C.8
(+) Add, subtract, and multiply matrices of appropriate dimensions.
- CCSS.Math.Content.HSN-VM.C.6
(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
- CCSS.Math.Content.HSN-VM.C.11
(+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations...
- CCSS.Math.Content.HSN-VM.B.5
(+) Multiply a vector by a scalar.