math-2017:1.G.3
math-2017:1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of or four of the shares in real-world contexts. Understand for these examples that decomposing into more equal shares creates smaller shares.
Learning goal: Partition circles and rectangles into two or four equal shares, name halves and fourths/quarters, describe a whole as two halves or four quarters, and compare the size of equal shares when the same whole is divided more finely. The word whole names the complete reference shape, while a shaded share names only a part of it.
Start with one paper rectangle representing a whole sandwich. Fold it into two equal areas. Each share is half of that whole. Two halves together reconstruct the whole. A line drawn anywhere does not guarantee halves: the two shares must be equal in size. Use folding or matching to check rather than only counting the regions.
Partition an equal-sized rectangle into four equal shares. Each is one fourth, also called one quarter, of its whole. All four quarters together make the whole. The illustration shades one part in each example. Its upper rectangle has one of two equal shares shaded—one half. The lower rectangle has one of four equal shares shaded—one quarter. Neither shaded amount is labeled as a whole.
Compare the blue areas only because the complete reference rectangles are the same size. A half is larger than a quarter of that same whole. Increasing the number of equal shares makes each share smaller in these examples. A half of a small object is not automatically larger than a quarter of a much larger object; first establish that the wholes match.
Use circles too. Fold a paper circle into two matching halves, then into four matching quarters. Trace the partitions and identify a single share, two halves together and four quarters together. The curved outside edges belong to the original circle; the interior lines separate equal shares. A shaded sector represents the chosen part, not a separate circular object.
Describe the real-world context carefully. If a picture represents one whole sandwich, the halves or quarters are shares of that one sandwich. Placing two sandwiches beside each other does not silently redefine both together as the original whole. For this first-grade lesson, concentrate on equal halves and quarters of a specified single circle or rectangle, using words and clear models.
Worked example 1: Half of a rectangle. Fold a rectangle into two equal areas and shade one. Say “one half of the rectangle is shaded; the other half is not.” Rejoin or unfold both to explain that two halves make the whole. The unshaded half still belongs to the whole.
Worked example 2: Fourths of a circle. Fold a circle in half and then in half again. Open it to reveal four matching sectors. One is a quarter, and all four reconstruct the circle. Do not call an unequal sector a quarter merely because four regions exist.
Worked example 3: Compare equal wholes. Draw two same-sized rectangles, one in halves and one in quarters, shading one share of each. The half covers more area than the quarter. State the same-whole condition as part of the explanation, rather than presenting the comparison as a rule for unrelated objects.
Guided practice: Make both two-share and four-share partitions with rectangles and circles. Partners check equal areas by folding or matching and explain the vocabulary. Deliberately show an unequal split and ask what must be repaired before naming its regions halves or quarters.
Independent tasks: Draw or construct halves of a rectangle, quarters of a circle, a whole made from two halves and a whole made from four quarters. Compare one half and one quarter using matching whole shapes. Explain the amount shaded and unshaded in at least one example.
Assessment and feedback: Credit an equal partition, accurate share name, reconstruction of the whole and a justified same-whole comparison. If a child names the blue half “one whole,” point to the complete outer boundary and separately name the selected part. If counting regions replaces checking equality, fold or measure the areas with suitable concrete supports. Extend by finding a different-looking equal partition that still represents halves of the same rectangle.
An adult may read the prompts aloud. Answer independently with words, objects, drawings or a demonstration before opening the answer guide. Award 1 point for a correct result or claim and 1 point for a matching explanation or demonstration; where a question asks only for a result (a corrected sentence, a spelling, a count), a fully correct result earns both points, and the answer guide shows what a complete response contains. Record prompting separately. The total (two points per question) is local practice feedback, not an Ohio proficiency level.
Draw a circle and split it into four equal shares. Shade one share. Name the shaded share in two ways.
One fourth of the circle, also called one quarter of the circle. The four shares must be equal, for example made by two straight lines through the center that cross at square corners.
Draw a rectangle for a granola bar and split it into two equal shares. Mia eats one share. What part of the bar did she eat?
Half of the bar: one of two equal shares. The drawing needs one line that makes two shares of equal size.
A round pizza is cut into four equal shares. Describe the whole pizza using the shares.
The whole pizza is four fourths, also called four quarters, of the pizza.
A sandwich is cut into two equal shares. Describe the whole sandwich using the shares.
The whole sandwich is two halves.
Two pancakes are the same size. One is cut into two equal shares and the other into four equal shares. Which pancake has the larger shares? Explain.
The pancake cut into two. Cutting the same-size whole into more equal shares makes each share smaller, so a half is larger than a quarter.
A waffle is cut into four pieces, but one piece is much bigger than the others. Are the pieces fourths?
No. Fourths must be four equal shares of the whole waffle.
Is half of a small cookie always more than a quarter of a large cookie?
No. A half is sure to be larger than a quarter when both are shares of the same-size whole. When the wholes differ, a quarter of a much larger cookie can be as big as, or bigger than, half of a small one.