How Many Groups? (Part 2)

Warmup

In the fraction addition app below, if the denominators of the fractions are the same, simply add the numerators. If the denominators are not equal, try to make them equal before adding the fractions. When you type in your answer in the boxes, click . If it is correct, you’ll see a check mark. Then click . The percentage of the correct answer will display.

Activity #1

Investigating groups in Division.

In the applet below, the size of the divisor represented by the blue box can be increased using the red circle. This will happen only when it is less than the number it is dividing. The maximum number you can use in this applet is 12.

• Move the first slider to the right to increase the number you want to divide.
• Now, move the second slider to the right to increase the size of the divisor.
• Check the two boxes below.
• Now read your question again.
• To find out the number of groups, check the remaining boxes.
• Click to reset.
• Try other numbers by following the same steps above.

• Answer the questions below.

Activity #2

Investigating How Many Groups in a Division.

• Write a fraction or whole number as an answer for the question. If you get stuck, use the fraction strips.

(1.) How many s are in 2 ?

(2.) How many s are in 3 ?

(3.) How many s are in ?

(4.) 1 ÷ = ?

(5.) 2 ÷ = ?

(6.) 4 ÷ = ?

Activity #3

Write a Multiplication or Division Equation.

• For each situation below, draw a diagram using the applet for the relationship of the quantities to help you answer the question.
• Then write a multiplication equation or a division equation for the relationship.

(1.) The distance around a park is miles. Noah rode his bicycle around the park for a total of 3 miles.

(a.) How many times around the park did he ride?

(b.) Write a multiplication equation or a division equation for the relationship.

(2.) You need yard of ribbon for one gift box. You have 3 yards of ribbon.

(a.) How many gift boxes do you have ribbon for?

(b.) Write a multiplication equation or a division equation for the relationship.

(3.) The water hose fills a bucket at gallon per minute.

(a.) How many minutes does it take to fill a 2-gallon bucket?

(b.) Write a multiplication equation or a division equation for the relationship.

Challenge #1

Use the standard inch ruler to answer the following question. Then, write a multiplication equation and a division equation that answer the question.

How many s are in 7?

Challenge #2

Use the pattern blocks in the applet to answer the question that follows. (If you need help aligning the pieces, you can turn on the grid.)

Challenge #3

Use the tape diagram to find the value of ½ ÷ ⅓ . Show your reasoning.