Section B: Practice Problems Halves, Thirds, and Fourths
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?
Problem 1 (Lesson 6)
Here is a pattern block shape Lin made.
Describe the blocks Lin used to make her shape.
Build Lin’s shape using only equal-size shapes.
Problem 2 (Lesson 7)
Andre drew this picture and said each part of the square is a fourth. Do you agree with Andre? Explain.
Partition the square into 4 equal parts in a different way.
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.
Problem 4 (Lesson 9)
Partition the circle into 4 equal parts.
Shade 3 parts blue and one part red.
How much of the circle is shaded?
Problem 5 (Exploration)
Is the square divided into fourths? Show your reasoning.
Problem 6 (Exploration)
Can you divide the square into equal parts?
4 equal parts with 3 of the parts different shapes
4 equal parts with 4 of the parts different shapes