Year 4: Fractions of shapes and sets

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. A fraction describes equal parts of a whole. Count all the equal parts for the bottom number. Count the parts you want for the top number.

1. Count ALL the equal parts in the whole. The bottom number of a fraction (the denominator) tells us how many equal parts there are altogether.
   There are 5 equal parts. The denominator is 5.
2. Count the parts that are shaded. The top number (the numerator) tells us how many parts we are talking about.
   2 parts are shaded. The numerator is 2.
3. Write the fraction. Put the numerator on top and the denominator on the bottom.
   25   (say “two fifths”)

Check. The parts that are shaded and the other parts together make all 5 parts: 2 + 3 = 5. ✓

Watch out. Count ALL the parts for the bottom number, not just the white ones.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. A fraction describes equal parts of a whole. Count all the equal parts for the bottom number. Count the parts you want for the top number.

1. Count ALL the equal parts in the whole. The bottom number of a fraction (the denominator) tells us how many equal parts there are altogether.
   There are 8 equal parts. The denominator is 8.
2. Count the parts that are shaded. The top number (the numerator) tells us how many parts we are talking about.
   5 parts are shaded. The numerator is 5.
3. Write the fraction. Put the numerator on top and the denominator on the bottom.
   58   (say “five eighths”)

Check. The parts that are shaded and the other parts together make all 8 parts: 5 + 3 = 8. ✓

Watch out. Count ALL the parts for the bottom number, not just the white ones.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. A fraction describes equal parts of a whole. Count all the equal parts for the bottom number. Count the parts you want for the top number.

1. Count ALL the equal parts in the whole. The bottom number of a fraction (the denominator) tells us how many equal parts there are altogether.
   There are 10 equal parts. The denominator is 10.
2. Count the parts that are shaded. The top number (the numerator) tells us how many parts we are talking about.
   3 parts are shaded. The numerator is 3.
3. Write the fraction. Put the numerator on top and the denominator on the bottom.
   310   (say “three tenths”)

Check. The parts that are shaded and the other parts together make all 10 parts: 3 + 7 = 10. ✓

Watch out. Count ALL the parts for the bottom number, not just the white ones.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. A fraction describes equal parts of a whole. Count all the equal parts for the bottom number. Count the parts you want for the top number.

1. Count ALL the equal parts in the whole. The bottom number of a fraction (the denominator) tells us how many equal parts there are altogether.
   There are 6 equal parts. The denominator is 6.
2. Count the parts that are shaded. The top number (the numerator) tells us how many parts we are talking about.
   5 parts are shaded. The numerator is 5.
3. Write the fraction. Put the numerator on top and the denominator on the bottom.
   56   (say “five sixths”)

Check. The parts that are shaded and the other parts together make all 6 parts: 5 + 1 = 6. ✓

Watch out. Count ALL the parts for the bottom number, not just the white ones.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. A fraction describes equal parts of a whole. Count all the equal parts for the bottom number. Count the parts you want for the top number.

1. Count ALL the equal parts in the whole. The bottom number of a fraction (the denominator) tells us how many equal parts there are altogether.
   There are 4 equal parts. The denominator is 4.
2. Count the parts that are shaded. The top number (the numerator) tells us how many parts we are talking about.
   3 parts are shaded. The numerator is 3.
3. Write the fraction. Put the numerator on top and the denominator on the bottom.
   34   (say “three quarters”)

Check. The parts that are shaded and the other parts together make all 4 parts: 3 + 1 = 4. ✓

Watch out. Count ALL the parts for the bottom number, not just the white ones.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. A fraction describes equal parts of a whole. Count all the equal parts for the bottom number. Count the parts you want for the top number.

1. Count ALL the equal parts in the whole. The bottom number of a fraction (the denominator) tells us how many equal parts there are altogether.
   There are 9 equal parts. The denominator is 9.
2. Count the parts that are shaded. The top number (the numerator) tells us how many parts we are talking about.
   4 parts are shaded. The numerator is 4.
3. Write the fraction. Put the numerator on top and the denominator on the bottom.
   49   (say “four ninths”)

Check. The parts that are shaded and the other parts together make all 9 parts: 4 + 5 = 9. ✓

Watch out. Count ALL the parts for the bottom number, not just the white ones.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. The bottom number comes from the kind of part (halves, thirds, quarters...). The top number comes from the number word.

1. What kind of part is it? “quarters” means the whole is cut into 4 equal parts. This is the bottom number.
   quarters → denominator 4
2. What is the number word? “three”. This is the top number.
   three → numerator 3
3. Write the fraction.
   34

Check. Say it back: 34 is three quarters. ✓

Watch out. “quarters” means the whole is cut into 4 equal parts. Check the kind of part before you write the bottom number.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. The bottom number comes from the kind of part (halves, thirds, quarters...). The top number comes from the number word.

1. What kind of part is it? “fifths” means the whole is cut into 5 equal parts. This is the bottom number.
   fifths → denominator 5
2. What is the number word? “two”. This is the top number.
   two → numerator 2
3. Write the fraction.
   25

Check. Say it back: 25 is two fifths. ✓

Watch out. “fifths” means the whole is cut into 5 equal parts. Check the kind of part before you write the bottom number.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. The bottom number comes from the kind of part (halves, thirds, quarters...). The top number comes from the number word.

1. What kind of part is it? “eighths” means the whole is cut into 8 equal parts. This is the bottom number.
   eighths → denominator 8
2. What is the number word? “five”. This is the top number.
   five → numerator 5
3. Write the fraction.
   58

Check. Say it back: 58 is five eighths. ✓

Watch out. “eighths” means the whole is cut into 8 equal parts. Check the kind of part before you write the bottom number.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. The bottom number comes from the kind of part (halves, thirds, quarters...). The top number comes from the number word.

1. What kind of part is it? “tenths” means the whole is cut into 10 equal parts. This is the bottom number.
   tenths → denominator 10
2. What is the number word? “seven”. This is the top number.
   seven → numerator 7
3. Write the fraction.
   710

Check. Say it back: 710 is seven tenths. ✓

Watch out. “tenths” means the whole is cut into 10 equal parts. Check the kind of part before you write the bottom number.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. The bottom number comes from the kind of part (halves, thirds, quarters...). The top number comes from the number word.

1. What kind of part is it? “sixth” means the whole is cut into 6 equal parts. This is the bottom number.
   sixth → denominator 6
2. What is the number word? “one”. This is the top number.
   one → numerator 1
3. Write the fraction.
   16

Check. Say it back: 16 is one sixth. ✓

Watch out. “sixths” means the whole is cut into 6 equal parts. Check the kind of part before you write the bottom number.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. The bottom number comes from the kind of part (halves, thirds, quarters...). The top number comes from the number word.

1. What kind of part is it? “thirds” means the whole is cut into 3 equal parts. This is the bottom number.
   thirds → denominator 3
2. What is the number word? “two”. This is the top number.
   two → numerator 2
3. Write the fraction.
   23

Check. Say it back: 23 is two thirds. ✓

Watch out. “thirds” means the whole is cut into 3 equal parts. Check the kind of part before you write the bottom number.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. Read the bottom number to find the kind of part. Read the top number to say how many.

1. Look at the bottom number: 4. The whole is cut into 4 equal parts. Parts like this are called quarters.
   4 → quarters
2. Look at the top number: 1. This is how many parts we have.
   1 → one
3. Put the words together.
   one quarter

Check. Write it back as numbers: one quarter is 14. ✓

Watch out. Say the top number first, then the kind of part.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. Read the bottom number to find the kind of part. Read the top number to say how many.

1. Look at the bottom number: 3. The whole is cut into 3 equal parts. Parts like this are called thirds.
   3 → thirds
2. Look at the top number: 2. This is how many parts we have.
   2 → two
3. Put the words together.
   two thirds

Check. Write it back as numbers: two thirds is 23. ✓

Watch out. Say the top number first, then the kind of part.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. Read the bottom number to find the kind of part. Read the top number to say how many.

1. Look at the bottom number: 6. The whole is cut into 6 equal parts. Parts like this are called sixths.
   6 → sixths
2. Look at the top number: 5. This is how many parts we have.
   5 → five
3. Put the words together.
   five sixths

Check. Write it back as numbers: five sixths is 56. ✓

Watch out. Say the top number first, then the kind of part.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. Read the bottom number to find the kind of part. Read the top number to say how many.

1. Look at the bottom number: 8. The whole is cut into 8 equal parts. Parts like this are called eighths.
   8 → eighths
2. Look at the top number: 3. This is how many parts we have.
   3 → three
3. Put the words together.
   three eighths

Check. Write it back as numbers: three eighths is 38. ✓

Watch out. Say the top number first, then the kind of part.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. Read the bottom number to find the kind of part. Read the top number to say how many.

1. Look at the bottom number: 10. The whole is cut into 10 equal parts. Parts like this are called tenths.
   10 → tenths
2. Look at the top number: 9. This is how many parts we have.
   9 → nine
3. Put the words together.
   nine tenths

Check. Write it back as numbers: nine tenths is 910. ✓

Watch out. Say the top number first, then the kind of part.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. Read the bottom number to find the kind of part. Read the top number to say how many.

1. Look at the bottom number: 5. The whole is cut into 5 equal parts. Parts like this are called fifths.
   5 → fifths
2. Look at the top number: 4. This is how many parts we have.
   4 → four
3. Put the words together.
   four fifths

Check. Write it back as numbers: four fifths is 45. ✓

Watch out. Say the top number first, then the kind of part.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. The bottom number tells us how many equal parts the whole is cut into. The top number tells us how many to shade.

1. Look at the bottom number of 35. It is 5, so the whole must be cut into 5 equal parts.
   The picture has 5 equal parts. ✓
2. Look at the top number. This is how many parts to shade.
   The top number is 3.
3. Write the answer.
   Shade 3 of the 5 parts.

Check. Count again: 3 shaded and 2 white make 5 parts. ✓

Watch out. The bottom number is the total number of parts. Do not shade that many!

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. The bottom number tells us how many equal parts the whole is cut into. The top number tells us how many to shade.

1. Look at the bottom number of 58. It is 8, so the whole must be cut into 8 equal parts.
   The picture has 8 equal parts. ✓
2. Look at the top number. This is how many parts to shade.
   The top number is 5.
3. Write the answer.
   Shade 5 of the 8 parts.

Check. Count again: 5 shaded and 3 white make 8 parts. ✓

Watch out. The bottom number is the total number of parts. Do not shade that many!

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. The bottom number tells us how many equal parts the whole is cut into. The top number tells us how many to shade.

1. Look at the bottom number of 710. It is 10, so the whole must be cut into 10 equal parts.
   The picture has 10 equal parts. ✓
2. Look at the top number. This is how many parts to shade.
   The top number is 7.
3. Write the answer.
   Shade 7 of the 10 parts.

Check. Count again: 7 shaded and 3 white make 10 parts. ✓

Watch out. The bottom number is the total number of parts. Do not shade that many!

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. Count all the equal parts for the bottom number. Count the parts that are NOT shaded for the top number.

1. Count ALL the equal parts. This is the bottom number (denominator).
   There are 8 equal parts altogether.
2. Count the parts that are NOT shaded. These are the white parts.
   8 − 3 = 5. So 5 parts are not shaded.
3. Write the fraction. The white parts go on the top. The total number of parts goes on the bottom.
   58

Check. Shaded + not shaded: 38 + 58 = 88 = 1 whole. ✓

Watch out. The question asks for the parts that are not shaded, so count the white ones.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. Count all the equal parts for the bottom number. Count the parts that are NOT shaded for the top number.

1. Count ALL the equal parts. This is the bottom number (denominator).
   There are 5 equal parts altogether.
2. Count the parts that are NOT shaded. These are the white parts.
   5 − 2 = 3. So 3 parts are not shaded.
3. Write the fraction. The white parts go on the top. The total number of parts goes on the bottom.
   35

Check. Shaded + not shaded: 25 + 35 = 55 = 1 whole. ✓

Watch out. The question asks for the parts that are not shaded, so count the white ones.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. Count all the equal parts for the bottom number. Count the parts that are NOT shaded for the top number.

1. Count ALL the equal parts. This is the bottom number (denominator).
   There are 6 equal parts altogether.
2. Count the parts that are NOT shaded. These are the white parts.
   6 − 1 = 5. So 5 parts are not shaded.
3. Write the fraction. The white parts go on the top. The total number of parts goes on the bottom.
   56

Check. Shaded + not shaded: 16 + 56 = 66 = 1 whole. ✓

Watch out. The question asks for the parts that are not shaded, so count the white ones.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. Count all the equal parts for the bottom number. Count the parts that are NOT shaded for the top number.

1. Count ALL the equal parts. This is the bottom number (denominator).
   There are 10 equal parts altogether.
2. Count the parts that are NOT shaded. These are the white parts.
   10 − 9 = 1. So 1 part is not shaded.
3. Write the fraction. The white parts go on the top. The total number of parts goes on the bottom.
   110

Check. Shaded + not shaded: 910 + 110 = 1010 = 1 whole. ✓

Watch out. The question asks for the parts that are not shaded, so count the white ones.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. A fraction of a set compares the part with the whole set. The total goes on the bottom and the part you want goes on the top.

1. Count ALL the counters. The total goes on the bottom of the fraction.
   red: 3
   blue: 5
   Total: 3 + 5 = 8
2. Count the red counters. This number goes on the top of the fraction.
   There are 3 red counters.
3. Write the fraction. 3 out of 8 is the fraction 3/8.
   38   (say “three eighths”)

Check. Add the fractions of every colour: the tops add up to 8, so the fractions together make 88 = 1 whole. ✓

Watch out. The bottom number is the whole set (8), not the number of the other colours.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. A fraction of a set compares the part with the whole set. The total goes on the bottom and the part you want goes on the top.

1. Count ALL the counters. The total goes on the bottom of the fraction.
   green: 7
   yellow: 3
   Total: 7 + 3 = 10
2. Count the yellow counters. This number goes on the top of the fraction.
   There are 3 yellow counters.
3. Write the fraction. 3 out of 10 is the fraction 3/10.
   310   (say “three tenths”)

Check. Add the fractions of every colour: the tops add up to 10, so the fractions together make 1010 = 1 whole. ✓

Watch out. The bottom number is the whole set (10), not the number of the other colours.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. A fraction of a set compares the part with the whole set. The total goes on the bottom and the part you want goes on the top.

1. Count ALL the counters. The total goes on the bottom of the fraction.
   red: 2
   blue: 4
   green: 3
   Total: 2 + 4 + 3 = 9
2. Count the blue counters. This number goes on the top of the fraction.
   There are 4 blue counters.
3. Write the fraction. 4 out of 9 is the fraction 4/9.
   49   (say “four ninths”)

Check. Add the fractions of every colour: the tops add up to 9, so the fractions together make 99 = 1 whole. ✓

Watch out. The bottom number is the whole set (9), not the number of the other colours.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. A fraction of a set compares the part with the whole set. The total goes on the bottom and the part you want goes on the top.

1. Count ALL the counters. The total goes on the bottom of the fraction.
   yellow: 5
   purple: 6
   Total: 5 + 6 = 11
2. Count the purple counters. This number goes on the top of the fraction.
   There are 6 purple counters.
3. Write the fraction. 6 out of 11 is the fraction 6/11.
   611   (say “six elevenths”)

Check. Add the fractions of every colour: the tops add up to 11, so the fractions together make 1111 = 1 whole. ✓

Watch out. The bottom number is the whole set (11), not the number of the other colours.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. A fraction describes equal parts of a whole. Count all the equal parts for the bottom number. Count the parts you want for the top number.

1. Count ALL the equal parts in the whole. The bottom number of a fraction (the denominator) tells us how many equal parts there are altogether.
   There are 4 equal groups. The denominator is 4.
2. Count the groups that are red. The top number (the numerator) tells us how many parts we are talking about.
   3 groups are red. The numerator is 3.
3. Write the fraction. Put the numerator on top and the denominator on the bottom.
   34   (say “three quarters”)

Check. The parts that are red and the other parts together make all 4 parts: 3 + 1 = 4. ✓

Watch out. Count ALL the parts for the bottom number, not just the white ones.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. A fraction describes equal parts of a whole. Count all the equal parts for the bottom number. Count the parts you want for the top number.

1. Count ALL the equal parts in the whole. The bottom number of a fraction (the denominator) tells us how many equal parts there are altogether.
   There are 5 equal groups. The denominator is 5.
2. Count the groups that are red. The top number (the numerator) tells us how many parts we are talking about.
   2 groups are red. The numerator is 2.
3. Write the fraction. Put the numerator on top and the denominator on the bottom.
   25   (say “two fifths”)

Check. The parts that are red and the other parts together make all 5 parts: 2 + 3 = 5. ✓

Watch out. Count ALL the parts for the bottom number, not just the white ones.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. A fraction describes equal parts of a whole. Count all the equal parts for the bottom number. Count the parts you want for the top number.

1. Count ALL the equal parts in the whole. The bottom number of a fraction (the denominator) tells us how many equal parts there are altogether.
   There are 6 equal groups. The denominator is 6.
2. Count the groups that are red. The top number (the numerator) tells us how many parts we are talking about.
   5 groups are red. The numerator is 5.
3. Write the fraction. Put the numerator on top and the denominator on the bottom.
   56   (say “five sixths”)

Check. The parts that are red and the other parts together make all 6 parts: 5 + 1 = 6. ✓

Watch out. Count ALL the parts for the bottom number, not just the white ones.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. A fraction describes equal parts of a whole. Count all the equal parts for the bottom number. Count the parts you want for the top number.

1. Count ALL the equal parts in the whole. The bottom number of a fraction (the denominator) tells us how many equal parts there are altogether.
   There are 8 equal slices. The denominator is 8.
2. Count the slices that are eaten by Noah. The top number (the numerator) tells us how many parts we are talking about.
   3 slices are eaten by Noah. The numerator is 3.
3. Write the fraction. Put the numerator on top and the denominator on the bottom.
   38   (say “three eighths”)

Check. The parts that are eaten by Noah and the other parts together make all 8 parts: 3 + 5 = 8. ✓

Watch out. Count ALL the parts for the bottom number, not just the white ones.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. A fraction describes equal parts of a whole. Count all the equal parts for the bottom number. Count the parts you want for the top number.

1. Count ALL the equal parts in the whole. The bottom number of a fraction (the denominator) tells us how many equal parts there are altogether.
   There are 8 equal slices. The denominator is 8.
2. Count the slices that are eaten by Mei. The top number (the numerator) tells us how many parts we are talking about.
   1 slice is eaten by Mei. The numerator is 1.
3. Write the fraction. Put the numerator on top and the denominator on the bottom.
   18   (say “one eighth”)

Check. The parts that are eaten by Mei and the other parts together make all 8 parts: 1 + 7 = 8. ✓

Watch out. Count ALL the parts for the bottom number, not just the white ones.

Key words. The denominator (bottom number) is how many equal parts. The numerator (top number) is how many parts we have.

Method. Count all the equal parts for the bottom number. Count the parts that are NOT shaded for the top number.

1. Count ALL the equal parts. This is the bottom number (denominator).
   There are 8 equal slices altogether.
2. Count the parts that are NOT eaten by Noah. These are the white parts.
   8 − 3 = 5. So 5 slices are not eaten by Noah.
3. Write the fraction. The white parts go on the top. The total number of parts goes on the bottom.
   58

Check. Eaten by noah + not eaten by Noah: 38 + 58 = 88 = 1 whole. ✓

Watch out. The question asks for the parts that are not shaded, so count the white ones.