Solve division problems that involve remainders.

Number Framework Stage 7

#### Using Number Properties

Problem: “Michael builds a string of beads using 3 colours, starting at white, black, then red then repeating the pattern.

He continues building using 103 beads altogether. What colour is the last bead?” *(Possible answer: 103 ÷* *3 = 34 remainder 1. So there are 34 groups of 3 and the last one is white.)*

Discuss what colour the last one will be if the remainder is 1, 2, or 0.

Examples: Find the colour of the last bead if there are these numbers of beads: 56 123 678 828 8 987

#### Understanding Number Properties:

Make up a bead problem like Michael’s where the number of beads is over 10 000.

Problem: “Michael builds a pattern of counters with four colours A, B, C, and D. So the counters look like ABCD ABCD ABCD ABCD .... What colour is the 45 679th bead?”

*(Possible answer: By calculator: 45 679 ÷* *4 =11419.75. The last bead will be C.)*

Example: Find the colour of the last bead if there are these numbers of beads: 5 489 12 788 823 451 34 500 28 987

Problem: “Starting at 12 o’clock, Michael records the hour hand of a 12-hour clock going around for 12 345 hours. What time does the clock show at the end of the 12 345 hours?”