Numerical and Algebraic Expressions: math practice, Grade 6 – download the PDF

1 Reading exponents ★★★

Write each power as a repeated multiplication, then find its value.

1. \(3^4\)
2. \(2^6\)
3. \(10^5\)
4. \(7^2\)

2 Order of operations ★★★

Find the value of each expression.

1. \(8 + 6 \cdot 3\)
2. \((8 + 6) \cdot 3\)
3. \(30 - 12 \div 4\)
4. \(5 \cdot 2^2\)

3 Words to expressions ★★★

Write an algebraic expression for each phrase.

1. 9 more than a number \(n\)
2. 4 times a number \(y\)
3. a number \(k\) decreased by 6
4. the quotient of \(m\) and 5

4 Evaluate with one variable ★★★

Evaluate each expression when \(x = 6\).

1. \(x + 9\)
2. \(4x\)
3. \(30 - x\)
4. \(\dfrac{x}{3}\)

5 Name the parts ★★★

Look at the expression \(7a + 3b + 12\).

1. How many terms does it have? List them.
2. What is the coefficient of \(a\)? Of \(b\)?
3. Which term is the constant?

6 Sort the like terms ★★★

Here are six terms: \(5x\), \(3y\), \(8\), \(2x\), \(9y\), \(4\). Group them into sets of like terms and tell what makes each set “like.”

7 True or false? ★★★

Decide whether each statement is true or false, and justify your answer.

1. \(2^3 = 6\)
2. \(4 + 3 \cdot 2 = 14\)
3. \(5(2 + 1) = 5 \cdot 2 + 5 \cdot 1\)
4. \(12 - 4 - 2 = 12 - (4 - 2)\)

8 Several operations ★★★

Find the value of each expression. Show every step.

1. \(3 + 2 \cdot (7 - 4)^2\)
2. \(48 \div 2^3 + 5 \cdot 4\)
3. \((12 - 4)^2 \div 16\)

9 Pizza party ★★★

Each pizza is cut into 8 slices. A party orders \(p\) pizzas.

1. Write an expression for the total number of slices.
2. How many slices are there if \(p = 3\), \(p = 5\), and \(p = 12\)?
3. The party wants 72 slices. Test \(p = 8\) and \(p = 9\) to find how many pizzas to order.

10 Saving money ★★★

Mia already has 40 dollars and saves 15 dollars each week for \(w\) weeks.

1. Write an expression for the amount she has after \(w\) weeks.
2. How much does she have after 8 weeks? After 12 weeks?
3. Name the coefficient and the constant in your expression.

11 Two variables ★★★

Evaluate each expression when \(a = 5\) and \(b = 3\).

1. \(2a + 4b\)
2. \(a^2 - b^2\)
3. \(3(a + b)\)

12 Expand with the distributive property ★★★

Use the distributive property to rewrite each expression without parentheses.

1. \(6(x + 4)\)
2. \(3(2y + 5)\)
3. \(7(n - 2)\)

13 Combine like terms ★★★

Simplify each expression by combining like terms.

1. \(7x + 3x\)
2. \(9y - 4y + 2\)
3. \(5a + 2b + 3a + b\)

14 Equivalent or not? ★★★

For each pair, test the value given, then decide whether the expressions are equivalent and explain.

1. \(3(x + 2)\) and \(3x + 2\), with \(x = 4\)
2. \(2x + x\) and \(3x\), with \(x = 5\)
3. \(4(x + 1)\) and \(4x + 4\), with \(x = 10\)

15 Factor out the common factor ★★★

Use the greatest common factor to rewrite each sum as a product.

1. \(12x + 18\)
2. \(20y + 30\)
3. \(35 + 14\)

16 Phone plan ★★★

A phone plan costs 20 dollars per month plus 4 dollars for each extra gigabyte \(g\) of data.

1. Write an expression for the monthly cost.
2. Find the cost for \(g = 0\), \(g = 3\), and \(g = 6\).
3. One month the bill is 48 dollars. How many extra gigabytes were used? Check your answer.

17 Expand, then simplify ★★★

Simplify \(5(x + 2) + 3x - 4\), then check your result when \(x = 3\).

18 Area and perimeter of a rectangle ★★★

A rectangle has width 3 and length \(x + 5\) (in feet).

1. Write expressions for its area and its perimeter, and simplify them.
2. Evaluate both when \(x = 4\).

19 Find the errors ★★★

Leo made three mistakes. Find each one, then correct it.

1. \(4(x + 3) = 4x + 3\)
2. \(2^4 = 8\)
3. \(5 + 2x = 7x\)

20 Prove an equivalence ★★★

Is \(2(3x + 4) - 2x\) equivalent to \(4x + 8\)? First fill a value table for \(x = 1, 2, 3\), then explain with properties.

21 Complex phrases ★★★

Write an expression for each phrase, then evaluate it for the value given.

1. Three times the sum of a number \(n\) and 8, decreased by 5 (\(n = 4\))
2. The square of \(m\) plus twice \(m\) (\(m = 5\))
3. Half of the sum of \(a\) and 10 (\(a = 6\))