Write, read, and evaluate expressions in which letters stand for numbers.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Letters standing for numbers is the big step into algebra, and sixth grade takes it in three parts. Part a is translation: turning words into symbols, so 'subtract y from 5' becomes 5 - y and 'twice a number, plus 3' becomes 2n + 3. Order matters in subtraction and division, which is why 'subtract y from 5' is not y - 5.
Part b gives students the vocabulary to talk about expressions: sum, term, product, factor, quotient and coefficient. In 4x + 7, there are two terms, 4x and 7, and the coefficient of x is 4. Students also learn to see a group as one object, so 2(8 + 7) is a product of two factors, one of which is itself a sum. Part c is evaluation: substituting a value for each variable and following the order of operations. This includes real formulas, like using V = s³ and A = 6s² to find the volume and surface area of a cube with side length 1/2.
'5 less than x' is x - 5, not 5 - x. Have students test with a number: 5 less than 12 is 7, which is 12 - 5.
When x = 4, some students write 3x as 34. 3x means 3 × x, so it equals 12.
In 8m, the coefficient is 8, the number multiplying the variable. The letter m is the variable.
Evaluating 2x² at x = 3 as (2 × 3)² gives 36. The exponent belongs to x only: 2 × 3² = 18.
Use V = s³ and A = 6s² to find the volume and surface area of a cube with side length s = 1/2 inch.
Answer: V = 1/8 cubic inch and A = 3/2 square inches (1.5 in²).
Card sorts that match phrases to expressions work well for part a; include 'trap' pairs like 'x divided by 4' and '4 divided by x'. For part b, ask students to describe the same expression in several ways: 3(x + 2) is a product, and the second factor is a sum of two terms.
Assessment tasks commonly ask students to choose the expression that matches a description, name a coefficient, or evaluate a formula. Fractions and decimals as variable values appear regularly.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: B) 9 - y
Subtracting y from 9 starts with 9 and takes y away: 9 - y.
Answer: 25
Substitute: 4 × 7 - 3 = 28 - 3 = 25.
Answer: D) 2
The coefficient is the number multiplying the variable. In 2y it is 2.
Answer: 17
a² = 4, so 3 × 4 + 5 = 12 + 5 = 17.
Answer: B) 3
Terms are separated by addition or subtraction: 6m, 4 and 2n. There are 3 terms.
Answer: 34
A = 8.5 × 4 = 34 square centimeters.
A full lesson with slides, activities and an exit ticket on writing, reading and evaluating expressions, pitched to grade 6 and editable in PowerPoint or Google Slides.
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Make a worksheet →Turn writing, reading and evaluating expressions into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Sum, term, product, factor, quotient and coefficient. Students should use these words to describe parts of expressions.
Yes. The standard's own example uses a cube with side length 1/2, so fraction and decimal values are expected.