Year 2: Two quarters are the same as one half

Method. Compare the amounts. If the shaded amounts are the same, the fractions are equal.

1. Look at 1/2. 1 of the 2 equal parts is one half.
   1/2
2. Look at 2/4. 2 of the 4 equal parts is two quarters.
   2/4
3. Compare the amounts. The same amount shaded means the fractions are equal.
   1/2 = 2/4
4. Decide.
   Yes. 1/2 is the same as 2/4.

Check. Make both amounts with equal parts and compare them side by side. ✓

Watch out. More parts does not always mean a bigger amount. Compare the shaded amounts.

Method. Two quarters make one half, so the two shaded amounts match.

1. Look at the shading. Two of the four equal parts are shaded.
   2/4 shaded
2. Find the matching half. Two quarters are the same as one half.
   2/4 = 1/2
3. Write the answer.
   1/2

Check. Two quarters and one half fill the same space. ✓

Watch out. Look for the fraction that is the same amount.

Method. Compare the amounts. If the shaded amounts are the same, the fractions are equal.

1. Look at 3/4. 3 of the 4 equal parts is three quarters.
   3/4
2. Look at 1/2. 1 of the 2 equal parts is one half.
   1/2
3. Compare the amounts. The same amount shaded means the fractions are equal.
   3/4 ≠ 1/2
4. Decide.
   No. 3/4 is not the same as 1/2.

Check. Make both amounts with equal parts and compare them side by side. ✓

Watch out. More parts does not always mean a bigger amount. Compare the shaded amounts.

Method. Count the quarters that make one half.

1. Count the quarters. One half needs 2 quarters.
   2 quarters
2. Put two quarters together. Two quarters fill half of the bar.
   1/4 + 1/4 = 2/4
3. Write the answer.
   1/2

Check. 2/4 and 1/2 are the same amount. ✓

Watch out. Two quarters make one half.

Key words. Two quarters means 2 of the 4 equal parts.

Method. Share into 4 equal plates, then take the ones you need.

1. Share the 12 sweets into 4 equal plates. Every plate needs the same number.
   12 ÷ 4 = 3
2. Find what is in one plate. Each plate has 3 sweets.
   3 in one plate
3. Take 2 plates. two quarters means 2 of the 4 equal plates.
   3 × 2 = 6
4. Write the answer.
   6

Check. Put the plates back together: 3 + 3 + 3 + 3 = 12. ✓

Watch out. Make every plate the same size before you count. Then count the plates you need.

Key words. One half means 1 of the 2 equal parts.

Method. Share into 2 equal plates, then take the ones you need.

1. Share the 12 sweets into 2 equal plates. Every plate needs the same number.
   12 ÷ 2 = 6
2. Find what is in one plate. Each plate has 6 sweets.
   6 in one plate
3. Take one plate. One plate is one half of the whole.
   6

Check. Put the plates back together: 6 + 6 = 12. ✓

Watch out. Make every plate the same size before you count. Then count the plates you need.

Method. Work out both amounts. Compare them.

1. Work out 2/4 of 12. Share 12 into 4 equal plates. Take 2 plates: 3 + 3 = 6.
   2/4 of 12 = 6
2. Work out 1/2 of 12. Share 12 into 2 equal plates. Each plate has 6.
   1/2 of 12 = 6
3. Compare. Both amounts are 6.
   6 = 6
4. Decide.
   No. 2/4 of 12 and 1/2 of 12 are both 6.

Check. Two groups of 6 make 12, and so do four groups of 3. ✓

Watch out. Equal amounts can be found in different ways.

Key words. One half means 1 of the 2 equal parts.

Method. Share into 2 equal pieces, then take the ones you need.

1. Share the 10 cm into 2 equal pieces. Every piece needs the same number.
   10 ÷ 2 = 5
2. Find what is in one piece. Each piece has 5 cm.
   5 in one piece
3. Take one piece. One piece is one half of the whole.
   5

Check. Put the pieces back together: 5 + 5 = 10. ✓

Watch out. Make every piece the same size before you count. Then count the pieces you need.

Method. Look at each picture and find the one with two quarters shaded.

1. Look at A. Count the equal parts and the shaded parts.
   A: 4 equal parts, 2 shaded
2. Look at B. Count the equal parts and the shaded parts.
   B: 4 equal parts, 1 shaded
3. Look at C. Count the equal parts and the shaded parts.
   C: 4 equal parts, 3 shaded
4. Find the picture that matches. We want the picture with two quarters shaded.
   Matches: A
5. Write the answer.
   A

Check. B and C do not match. ✓

Watch out. Count the equal parts first, then the shaded parts.

Method. Compare the amounts. If the shaded amounts are the same, the fractions are equal.

1. Look at 2/4. 2 of the 4 equal parts is two quarters.
   2/4
2. Look at 1/2. 1 of the 2 equal parts is one half.
   1/2
3. Compare the amounts. The same amount shaded means the fractions are equal.
   2/4 = 1/2
4. Decide.
   Yes. 2/4 is the same as 1/2.

Check. Make both amounts with equal parts and compare them side by side. ✓

Watch out. More parts does not always mean a bigger amount. Compare the shaded amounts.

Method. Compare the shaded amounts, not the bottom numbers.

1. Look at 1/2. One half is one of two equal parts.
   1 of 2 parts
2. Look at 2/4. Two quarters fill the same amount as one half.
   2 of 4 parts
3. Compare. The two shaded amounts are the same.
   2/4 = 1/2
4. Decide.
   No. 2/4 and 1/2 are the same amount.

Check. Two quarters make one half, so they are equal. ✓

Watch out. A bigger bottom number does not mean a bigger amount.

Method. Compare the shaded parts.

1. Look at Ruby. Ruby eats one half of the pizza.
   1/2
2. Look at Sam. Sam eats two quarters of the pizza.
   2/4
3. Compare. Two quarters make one half.
   2/4 = 1/2
4. Decide.
   Same. One half and two quarters are equal.

Check. Two quarters are the same amount as one half. ✓

Watch out. Compare the shaded amounts, not the number of parts.