Section B: Practice Problems Halves, Thirds, and Fourths

Section Summary

Details

We have learned a lot about composing and decomposing shapes. Sometimes the pieces make up a whole shape, but all of the pieces are not the same size. Sometimes the whole is partitioned into equal pieces and they have special names. We practiced partitioning shapes into halves, thirds, and fourths. We learned that halves, thirds, and fourths of the same shape can look different. We learned that we can say the whole shape is 2 halves, 3 thirds, 4 fourths, or 4 quarters.

How can you use halves, thirds, fourths, or quarters to describe the pieces of these shapes? How can you use halves, thirds, fourths, or quarters to describe the whole shape?

Diagram. Circle partitioned in halves. One half shaded.
Diagram. Shaded square partitioned into four equal parts. 
Six-sided shape composed of two pattern blocks.
Six-sided shape composed of two pattern blocks.
Hexagon.
Diagram. Circle partitioned into fourths. One fourth shaded.

Problem 1 (Lesson 6)

Here is a pattern block shape Lin made.

Shape made of pattern blocks.

  1. Describe the blocks Lin used to make her shape.

  2. Build Lin’s shape using only equal-size shapes.

Problem 2 (Lesson 7)

  1. Andre drew this picture and said each part of the square is a fourth. Do you agree with Andre?  Explain.

    Diagram. Square partitioned into 4 equal parts.

  2. Partition the square into 4 equal parts in a different way.

    Square.

Problem 3 (Lesson 8)

Diego cut a square into two equal pieces and then cut one of the pieces into two equal pieces. He says the shaded part is a third of the square. Do you agree with Diego? Explain your reasoning.

Diagram. Square partitioned into 3 unequal parts, 1 part shaded.

Problem 4 (Lesson 9)

  1. Partition the circle into 4 equal parts.

  2. Shade 3 parts blue and one part red.

  3. How much of the circle is shaded?

Circle.

Problem 5 (Exploration)

Is the square divided into fourths? Show your reasoning.

Diagram. Square partitioned into 4 parts.

Problem 6 (Exploration)

Can you divide the square into equal parts?

  1. 4 equal parts with 3 of the parts different shapes

    Square.

  2. 4 equal parts with 4 of the parts different shapes

    Square.