Growth Point 6

Materials: Two dice and one set of cards numbered 1 to 5.

Activity: Students take turns to roll the dice and make a two-digit number. They then turn over a card and determine whether or not the number on the card will divide evenly into their two-digit number. If not, they are permitted to alter the order of their digits. For instance, a student who rolled 3 and 5 and made 53 could change it to 35 if that is more useful.

If their number will divide evenly, they score one point and play passes to the next person. If it will not divide, play passes to the next person with no score.

Related key ideas: Division with a remainder, properties of division.

Variation: Divide the number and state the remainder. The first student to score five points is the winner.

Materials: Calculator.

Activity: Students are permitted to enter only the digit 2 and these symbols on their calculator: ÷, ÷, ÷, ÷, =, =, =, = (i.e. they can press the division button four times, and the equals button four times). Using only these operations, what number would need to be entered in the first instance, so that the answer the calculator produces after the four division computations is 2?

Related key ideas: Properties of division.

Variation: Repeat the activity using any variation of numerals numbers and a different target number (e.g. 5, 10, 4, 1, 0). Can students find a pattern?

Materials: Deck of cards (picture cards removed), dice.

Activity: The aim of this game is to end up with as few counters as possible. Students take turns to draw two cards from the pack and make a two-digit number. They then roll the dice and divide this number into their two-digit number. At this point they could reverse the order of the digits if it suits them (e.g. a student who rolls 2 and makes 21 could change it to 12). If the number does not divide in evenly, the student must collect the remainder number of counters and play then moves to the next student. After a set time period, the student with the least total number of remainder counters is the winner.

Related key ideas: Division with a remainder, properties of division.

Materials: None.

Activity: Familiarise students with the game of ‘Clumps’. Ask students to imagine that they are leading a game of Clumps with some junior school students. They need to determine what size to make the groups for each round to ensure that only one person is left out each time.

For example, Round 1 begins, with 10 students. The instruction, ‘Make clumps of 3’ would make 3 groups of 3, using 9 students, with 1 student left out. In Round 2, with 9 students, the instruction, ‘Make clumps of 4’, would make 2 groups of 4, using 8 students, with 1 student left out. Continue Round 3 with 7 students.

Related key ideas: Division with a remainder, properties of division.

Variation: Is it possible to go through the above process, having only one student left out each round, using the total number of students for the year level? What would the clump sizes be?

Materials: Deck of cards(picture cards removed).

Activity: Each student draws four cards from a pile. The aim is to be the first to be able to use the four cards to make a correct division algorithm number sentence (e.g. use the cards 3, 2, 4 and 8 to make 32 ÷ 4 = 8). Play passes from student to student. If a student cannot make an algorithm, they can return one card to a central discard pile and collect another from the leftover cards face-down in the centre. When a student makes a correct algorithm, they score one point and all cards are returned to the centre and shuffled, ready to play again. The first student to score five points is the winner.

Note that, for instance, the 10-card with a 4-card could be read as 104.

Related key ideas: Properties of division.