B. Number · Number Sense: Numbers to 50 and FractionsHalves and Fourths
B1.7 B1.6About 30 minutes
Learning goals- I can cut a whole into 2 equal parts called halves.
- I can cut a whole into 4 equal parts called fourths.
- I can show that one half and two fourths of the same whole are the same amount.
Words to know
whole
One complete thing, like a whole pizza or a whole sandwich.
half
One of 2 equal parts of a whole. Two halves make one whole.
fourth
One of 4 equal parts of a whole. Four fourths make one whole. A fourth is also called a quarter.
equal parts
Parts that are exactly the same size.
Sharing one pizza
It's pizza night! There is one whole pizza. If 2 people share it fairly, how much does each person get? What if 4 people share it?
When we share one thing fairly, we cut it into equal parts. Today you will learn about two kinds of equal parts: halves and fourths.
This pizza is cut into 4 equal parts, so each slice is one fourth. Two slices together make one half. AI-generated imageHalves
When 2 people share one whole fairly, we cut the whole into 2 equal parts. Each part is called one half.
- 2 halves make 1 whole.
- Both halves must be the same size.
Fourths
When 4 people share one whole fairly, we cut the whole into 4 equal parts. Each part is called one fourth (or one quarter).
- 4 fourths make 1 whole.
- All four parts must be the same size.
Notice
A fourth is smaller than a half. When the same whole is shared by more people, each person gets a smaller piece.
Equal parts, different shapes
There is more than one way to cut a square into fourths! The parts look different, but each part is still one fourth of the whole, as long as all 4 parts are equal.
The big idea: one half is the same as two fourths
Look at two pizzas that are exactly the same size.
- The first pizza is cut into halves. Jada eats one half.
- The second pizza is cut into fourths. Owen eats two fourths.
Who ate more pizza?
They ate the same amount! If you put two fourths together, they fit exactly on top of one half.
One half and two fourths of the same whole are equal.
That's because each half can be cut into 2 equal pieces, and each of those pieces is one fourth. So one half = two fourths.
Worked exampleSharing two ways
Dad has one big pancake. Is it better to get one half of the pancake or two fourths of the same pancake?
- Draw the pancake. Cut it in half with one line. Colour one half.
- Draw the same pancake again. Cut it into fourths with two lines that cross. Colour two fourths.
- Compare the coloured parts. They cover the same amount of pancake.
It doesn't matter! One half and two fourths of the same pancake are the same amount.
Worked exampleIs it a half?
Ava folded a paper in half, and then folded it in half again. She opened it up and saw 4 equal parts. She coloured 2 of the parts. Did she colour half of the paper?
- Folding in half twice makes 4 equal parts, so each part is one fourth.
- Ava coloured 2 fourths.
- Two fourths is the same as one half.
Yes! Two fourths of the paper is one half of the paper.
Same whole
This only works for the same whole. One half of a tiny cookie is not the same as two fourths of a giant pizza! When we compare parts, the wholes must be the same size.
Just for funWhat did one half of a sandwich say to the other half?
"Together we make a great whole team!"
Hands-on activityFold and see
You need: 3 sheets of paper the same size, crayons, and scissors (with a grown-up's help).
- Fold the first sheet in half. Open it. Colour one half. Write "one half".
- Fold the second sheet in half, then in half again. Open it. How many parts? (4!) Colour one fourth.
- Fold the third sheet the same way into 4 parts. Colour two fourths.
- Put the "one half" sheet next to the "two fourths" sheet. What do you notice?
- Cut out the two coloured fourths and lay them on top of the coloured half. Do they cover it exactly?
Bonus: Try sharing a slice of toast or a tortilla into halves, then into fourths, at snack time.
Your turn!
1How many halves make one whole?
2How many fourths make one whole?
3A sandwich is cut into 2 pieces of different sizes. Is each piece one half?
No. Halves must be equal parts.
4Which is bigger: one half or one fourth of the same pizza?
One half. When a whole is cut into fewer pieces, each piece is bigger.
5How many fourths are the same as one half?
6Leo ate 2 fourths of an apple. Mia ate 1 half of the same size apple. Who ate more?
They ate the same amount. 2 fourths = 1 half.
74 friends share a pizza fairly. What part does each friend get?
Each friend gets one fourth of the pizza.
More practice: warm-up
1A pizza is cut into 2 equal parts. What is each part called?
2True or false: 4 fourths make one whole.
3An orange is cut into 4 equal pieces. Is each piece a half or a fourth?
A fourth, because there are 4 equal pieces.
4A sandwich is cut into halves. How many people can share it fairly?
5What is another name for one fourth?
More practice: on your own
1Jada ate one half of a pizza. Owen ate one fourth of a pizza that is the same size. Who ate more?
Jada. A half is bigger than a fourth, because the pizza was cut into fewer pieces.
2A square is cut into 4 triangles that are all exactly the same size. Is each triangle one fourth of the square?
Yes. The parts look different from small squares, but all 4 parts are equal, so each one is a fourth.
3Sam cut a pita into 4 pieces. Two pieces are big and two pieces are small. Are the pieces fourths?
No. Fourths must be 4 equal parts. These pieces are not the same size.
4How many fourths are in 2 halves?
4 fourths. Each half is 2 fourths, and 2 fourths and 2 fourths make 4 fourths. That is one whole!
5Ella folded a paper strip into 4 equal parts and coloured 2 of them. What part of the strip did she colour?
She coloured two fourths, which is the same as one half of the strip.
Challenge
1Find the mistake! Ben says one half of a small cookie is the same amount as two fourths of a giant pizza. Is he right? Explain.
No. One half and two fourths are only the same amount when they come from the same whole. Two fourths of a giant pizza is much more food than half of a small cookie.
2A pizza is cut into fourths. Dad eats 1 fourth and Mom eats 1 fourth. How much of the pizza did they eat altogether? How much is left?
They ate 2 fourths, which is one half of the pizza. 4 fourths take away 2 fourths leaves 2 fourths, so one half is left.
3How can you share one sandwich fairly among 4 people using only straight cuts? Explain your thinking.
Cut the sandwich in half first. Then cut each half in half again. Now there are 4 equal parts, so each person gets one fourth.
Quiz
1. A muffin is cut into 4 equal parts. What is each part called?
2. Which is the same amount as one half?
3. Which picture shows halves?
4. How many fourths make a whole?
5. A pizza is cut into 4 equal parts. Lia eats 2 parts. How much of the pizza did she eat?
6. Which is smaller: one half or one fourth of the same sandwich?
What your child is learning: that a whole can be shared fairly by cutting it into equal parts. Two equal parts are halves; four equal parts are fourths. The key idea is that one half and two fourths of the same whole are equal. Grade 1 students use words (one half, two fourths) rather than fraction symbols such as 1/2.
Common mistakes and how to help:
- Calling any two pieces "halves". In everyday speech we say "the bigger half", but in math halves are always equal. Cut food unevenly and ask "Are these halves?"
- Thinking a fourth is bigger than a half because 4 is bigger than 2. Cut two identical pieces of bread, one into halves and one into fourths, and compare the pieces.
- Thinking two fourths is more than one half because there are more pieces. Lay two fourths on top of one half to show they match.
- Comparing parts of different-size wholes. Always use the same size whole when comparing.
Everyday practice: fold napkins, cut sandwiches, share oranges or pizza. Ask "Is that a fair share?" "How much did each of us get?"
Math talk questions: "How do you know the parts are equal?" "Would you rather have one half or two fourths? Why?"