Show One Half in Two Ways
Recognize equivalent fractions using matching models.
Supplied materials
- Paper and pencil.
- Supplied matching strips: one has two equal parts, another has four.
Learn the idea
The same amount can have two fraction names. Shade one of two equal parts in the first strip. Shade two of four equal parts in a matching strip. Both shaded amounts reach halfway across the whole.
The fourths are smaller than the halves, so it takes two fourths to cover one half. Equivalent fractions have the same size and lie at the same place on a number line. The equality sign describes the amount, although the counts of pieces differ.
- Draw matching strips split into halves and fourths.
- Shade 1/2 in one and 2/4 in the other; compare shaded endpoints.
- Draw a matching strip in six parts and shade three to test another name for one half.
See the method in action
1/2 = 2/4 because one half covers exactly two fourths of the same whole. Three of six equal parts also cover half: 3/6 = 1/2.
Check your reasoning
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See the answer and explanation
1/2
Three shaded parts and three unshaded parts divide the strip into two equal amounts. Therefore 3/6 = 1/2.
Take it further
Use eight equal parts and shade four. The shaded and unshaded amounts each use four parts, so 4/8 = 1/2. Compare with the halves strip to check.
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