Fractions by Thirds

This square is one unit and it is split into smaller parts. Label each part with the fraction it shows.

How many green rectangles make one unit?

How many small red squares make one unit?

How many small blue rectangles make one unit?

How many small pink rectangles make one unit?

Which coloured bits would you use to show that three eighteenths equals one sixth? \frac{3}{18}=\frac{1}{6}

Which coloured bits would you use to show that two sixths equals one third? \frac{2}{6}=\frac{1}{3}

Which coloured bits would you use to show that one ninth plus two ninths equals one third? \frac{1}{9}+\frac{2}{9}=\frac{1}{3}. Why does this addition work that way?

You may find that this 3 by 3 grid helps you to answer the questions.

FRACTIONS BY THIRDS GAME

The game is for 2 players or 2 teams.

Copy the pattern onto thick card and cut it into 8 pieces: the outer frame and the seven coloued pieces: \frac{1}{3} (green),  \frac{2}{9} (yellow), \frac{1}{6} (blue), \frac{1}{9} (red), and \frac{1}{18} (pink).

Put in a bag seven idential cards with the fractions \frac{1}{3}, \frac{2}{9}, \frac{1}{6} and \frac{1}{9} on 4 of the cards and \frac{1}{18} on the other 3 cards.

The first player randomly picks 3 cards from the bag, selects the 3 coloured puzzle pieces that match the fractions on the cards, puts them in the frame and works out the corresponding total fraction. The second player picks 3 cards at random from the 4 remaining in the bag, puts them in the frame and works out his total. For example, a pink, a red and a blue piece make \frac{1}{18} +\frac{1}{9} + \frac{1}{6} =\frac{6}{18} = \frac{1}{3}. The players must agree the scores. Then the cards are returned to the bag.  The player with the highest total wins that round. The winner is the player with the highest total score after 5 rounds.

Draw your own pattern in a square and label the fractions in your pattern.

Click here to download the FRACTIONS BY THIRDS worksheet.

Click here to download the Notes for Teachers.