Guided Practice

Here are more examples of expressions.

Subtraction

two degrees less than 15°FExpression: 15 – 2

Multiplication

half as tall as my 6-foot-tall brotherExpression: 1/2× 6 (or 1/2 x 6)

Division

amount each person gets if 2.5 grams of chocolate is shared equally with 4 peopleExpression: 2.5 ÷ 4

An exponent expression has a base and an index.
^{2} = 3 × 3

5^{3} = 5 × 5 × 5

10^{1} = 10

2^{5} = 2 × 2 × 2 × 2 × 2

When the index is positive, it tells how many times to use the base as a factor in a multiplication expression.

35

10

2

"I have 2 apples, and you give me 2 more."

Write the expression that represents how many I have in all.

+"I have 2 apples, and you have twice as many apples."

Write the expression that represents how many you have in all.

×
Write the expression. Use +, -, x, or /.

You can type 83 words every minute.

How many can you type in 4 minutes?

Write the expression. Use +, -, x, or /.

You give away 14 carnival prizes out of the 60 you bought. How many are left?

Write the expression. Use +, -, x, or /.

There are 5 glasses, and you pour an equal amount from a 5.2-liter bottle into each glass until the bottle is empty. How much water is in each glass?

Write the expression. Use +, -, x, or /.

You have 160 phone minutes. How many three-minute calls can you make?

Write the expression. Use +, -, x, or /.

Bananas cost $1.25 per pound. How much does 2.4 pounds of bananas cost?

Write the expression as a single value.

3^{4} =

Write the expression as a single value.

4^{3} =

Write the expression as a single value.

1^{99} =

Write the expression as a single value.

0.5^{2} =

Each letter is a variable which stands for a whole number from two to twenty. (Numbers can be repeated.) Enter a calculation (press =) to see the numeric result. Press C to clear the result. You can use just one operation in a calculation. Keep track of your results in the notes box below the calculator display. Try to determine the value of all the variables.

The value of a is .

The value of b is .

The value of c is .

The value of d is .

The value of e is .

The value of f is .

The value of g is .

The value of h is .

The value of k is .

The value of m is .

The value of n is .

The value of p is .

The value of q is .

The value of r is .

The value of s is .

The value of t is .

The value of w is .

The value of x is .

The value of y is .

The value of z is .

Volume is the amount of space taken up by a three-dimensional object. The volume of a rectangular prism, which is shaped like a box, is calculated as length × width × height.

When the length, width, and height are all the same, the rectangular prism is a cube. The volume of a cube can be written with an exponent:

Volume = 2 × 2 × 2 = 2^{3}

^{3}

Area is the amount of space taken up by a two-dimensional object. The area of a square with side length s is s × s, or s^{2}.

The area of the square can be written with an exponent:

Area = 2 × 2 = 2^{2}

^{2}

A cube has side lengths of 5 in. Calculate the volume of the cube. Write the volume as a power and in standard form.

= in.^{3}

A cube has side lengths of 10 cm. Calculate the volume of the cube. Write the volume as a power and in standard form.

= cm^{3}

A cube has side lengths of 1/4 in. Calculate the volume of the cube. Write the volume as a power and as a fraction.

= cm^{3}

A square has side lengths of 3 in. Calculate the area of the square. Write the area as a power and in standard form.

= in.^{2}

A square has side lengths of 3/5 in. Calculate the area of the square. Write the area as a power and as a fraction.

= in.^{2}

A square has side lengths of 2/9 in. Calculate the area of the square. Write the area as a power and as a fraction.

= in.^{2}

A square has side lengths of 11 ft. Calculate the area of the square. Write the area as a power and in standard form.

= ft^{2}

The two cubes shown below both have the same length, width, and height. Write an expression using multiplication and exponents to describe the combined volume of the two cubes. Then write the volume in standard form. Evaluate the power before multiplying.

× = cm^{3}

The three cubes shown below all have the same length, width, and height. One side length is labeled. Write an expression using multiplication and exponents to describe the combined volume of the three cubes. Then write the volume as a fraction in simplest form. Evaluate the power before multiplying.

× = in.^{3}

The shaded squares shown all have the same side lengths. One side length is labeled. Write an expression using multiplication and exponents to describe the combined area of the shaded squares (not counting the white square). Then write the area in standard form. Evaluate the power before multiplying.

× = mm^{2}

The shaded squares shown all have the same side lengths. One side length is labeled. Write an expression using multiplication and exponents to describe the combined area of the shaded squares. Then write the area in standard form. Evaluate the power before multiplying.

× = mm^{2}

Play the Towers of Hanoi! Select 1, 2, 3, 4, or 5 discs to play. Move a disc to another peg by clicking on the peg you want to move from. Click to see the green triangle. Then click on the peg you want to move the disc to.

You have to move the top disk on a peg, and you aren't allowed to place a larger disc on top of a smaller disc.See if you can move all the discs from the starting peg to either of the other pegs in the minimum number of moves:

Discs | Moves |
---|---|

1 | 1 |

2 | 3 |

3 | 7 |

4 | 15 |

5 | 31 |

To convert a word problem into a numeric expression, it sometimes helps to look for certain words. The phrase "in all" might tell you that you can use addition (+), "left over" can mean to subtract (-), "times" can mean to multiply (x), and "equal groups" might mean division (/).

For example, if you have 4 cats and 3 dogs, how many animals do you have in all?

The expression 4 + 3 or 3 + 4 describes the number of animals in all.

Complete the expression. Use +, -, x, or /.

Trish has 14 quarters. She spends 9 of them. How many quarters does she have left over?

14 9