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Model Zoo

Create models to represent the fractions in the word problems.

Goal:

Goal:

View of a lion at the Smithsonian National Zoo in Washington, DC. The local zoo is doing a bit of remodeling. They need to divide some of their animal pens to accommodate some new animals. The zookeepers are making a plan to show the construction crew what they need. Use what you know about fraction models and division to create models the zookeepers can use to show their plans.

Here is an example to help you.

Currently, the elephants share 2 large pens. The zoo needs to divide the 2 original pens to make 4 new pens total. How much space will each new pen receive? This problem can be represented by the division expression 2 ÷ 4. As a model, that would look like:

Two green squares divided into two pieces.

Two spaces divided into four sections, 2 ÷ 4. As you can see with the model, each new pen will be \(\mathsf{ \frac{1}{2} }\) of an original pen.

So, \(\mathsf{ 2 \div 4 = \frac{1}{2} }\).

For each problem below, write a division expression, and create a model that represents the problem.

This problem can be represented by the division expression 4 ÷ 6. The 4 original pens are being divided into 6 new pens total. As a model, that would look like this:

Four horizontal bars divided into six pieces. Bar one: four blue and three red pieces. Bar two: two red and four yellow pieces. Bar three: four yellow and two green pieces. Bar four: two green and four pink pieces.

The 6 colors represent the 6 groups (new pens). Each new pen will be \(\mathsf{ \frac{4}{6} }\) of the old pens: \(\mathsf{ 4 \div 6 = \frac{4}{6} }\).

This problem can be represented by the division expression 1 ÷ 3. The 1 original lion pen is being divided into 3 new pens. The model representing this scenario would look like this:

One rectangle divided into three pieces; one pink, one yellow, and one green piece.

The 3 colors represent the 3 groups (new pens). Each new pen will be \(\mathsf{ \frac{1}{3} }\) of the old pen: \( 1 \div 3 = \mathsf{ \frac{1}{3} }\).

This problem can be represented by the division expression 5 ÷ 8. The 5 original giraffe stalls are being divided into 8 stalls. This is represented in the model below:

Five horizontal bars divided into eight pieces. Bar one: five red and three yellow pieces. Bar two: two yellow, five green, and one blue piece. Bar three: four blue and four light green pieces. Bar four: one light green five pink and two yellow pieces. Bar five: three yellow and five green pieces.

The 8 colors represent the 8 groups, or stalls. Each new stall will be \(\mathsf{ \frac{5}{8} }\) of the old pens: \(\mathsf{ 5 \div 8 = \frac{5}{8} }\) .