Chapter 6 — Practice examination

1/3 m of wire is shared equally among 3 projects. How much wire does one project receive? Use an exact equal-parts diagram.

Application-and-critique task: 1/3 m of insulated wire is divided evenly among 3 projects. How much wire does one project receive? Use an exact equal-parts diagram. Independently prepare one fraction bar split into exactly equal recipient shares; do not simply repeat the first application question’s computation. A student wrote this solution: “Dividing 1/3 by 3 means multiplying, so I wrote 1 instead of finding the right group size.” Is that reasoning valid? Name the first incorrect step; demonstrate a corrected computation and independently check it.

4/5 m of wire is shared equally among 2 projects. How much wire does one project receive? Use an exact equal-parts diagram.

Application-and-critique task: 3/4 m of craft wire is apportioned equally among 3 projects. How much wire does one project receive? Use an exact equal-parts diagram. Independently prepare a fraction bar distinguishing whole, number of people, and share; do not simply repeat the first application question’s computation. A student wrote this solution: “Dividing 3/4 by 3 means multiplying, so I wrote 9/4 instead of finding the right group size.” Is that reasoning valid? Name the first incorrect step; demonstrate a corrected computation and independently check it.

A classroom has 5 whole meters of tape. Each project uses 1/2 m. How many complete project pieces can be measured?

Application-and-critique task: An outdoor activity club has 5 whole meters of tape. Each project uses 1/4 m. How many complete project pieces can be measured? Independently prepare a group-count number line marking each fractional piece; do not simply repeat the first application question’s computation. A student wrote this solution: “5 ÷ 1/4 = 5/4; I multiplied instead of counting how many 1/4-size groups fit.” Is that reasoning valid? Name the first incorrect step; demonstrate a corrected computation and independently check it.

A workshop has 6 liters of paint. Each marked measuring cup holds 2/5 L. How many cup measures can be poured? A fractional final measure counts as part of a cup.

Application-and-critique task: A paint-mixing studio has 5 liters of paint. Each marked measuring cup holds 3/4 L. How many cup measures can be poured? A fractional final measure counts as part of a cup. Independently prepare a measurement number line including a possible partial group; do not simply repeat the first application question’s computation. A student wrote this solution: “5 ÷ 3/4 = 15/4; I multiplied instead of counting how many 3/4-size groups fit.” Is that reasoning valid? Name the first incorrect step; demonstrate a corrected computation and independently check it.

1/2 kg of modeling clay is divided equally among 2 makers. What is each maker’s share?

Application-and-critique task: 3/5 kg of sculpting clay is shared evenly among 5 makers. What is each maker’s share? Independently prepare both a sharing interpretation and an inverse multiplication check; do not simply repeat the first application question’s computation. A student wrote this solution: “Dividing 3/5 by 5 means multiplying, so I wrote 3 instead of finding the right group size.” Is that reasoning valid? Name the first incorrect step; demonstrate a corrected computation and independently check it.