Long Jumps

Using Equipment

Place three pegs of different colours at the number twenty-four on a number line. Tell  the students that the pegs represent different animals.  The green peg is a frog that can jump three spaces each time, the yellow peg is a leopard that can jump four spaces each time, and the orange peg is an antelope that can jumps six spaces each time. Demonstrate with the pegs how far each animal can jump.

Ask, Each animal wants to jump back to zero. How many jumps will they take to get there?

Get the students to predict how many jumps will be required and explain their reasoning. Look for students to apply their multiplication knowledge. For example, “Two sixes are twelve so four sixes are twenty-four so with four jumps the antelope can get to zero.”

If necessary, allow the students to jump pegs along the number line to check their predictions. Ask them to record the numbers each animal landed on and how many jumps were taken.

For example: the grasshopper

Record the results as division and equal subtraction equations:24 ÷ 3 = 8 and 24 – 3 – 3 – 3 – 3 – 3 – 3 – 3 - 3 = 0

Ask students where the eight can be found in the equal additions equation, that is the number of times three is taken away. Compare the equations for the leopard and antelope, 24 ÷ 4 = 6 and 24 ÷ 6 = 4, to see if students can identify the common factors. Pose similar jumping problems such as:

Three animals on twenty, the animals jump three, four, and five spaces respectively.How many jumps does each animal take to get to zero? Note that the three-jumper will go past zero.

This raises issues of complete jumps and part jumps. This could be recorded as,

20 ÷ 3 = 6 r 2 or 20 ÷ 3 = 6 2/3 or 20 – 3 – 3 – 3 – 3 – 3 – 3 – 2 = 0.

This also raises the issue of negative numbers as the antelope lands below zero with seven jumps.

Using Imaging

Pose jumps problems with the number line turned over so the numbers are not visible.

For example, Possum, cat, and dog are on the number eighteen. Possum jumps three spaces each time, cat jumps six spaces, and dog jumps nine. How many jumps will each animal take to reach zero?

Require the students to imagine the jumps taken and which numbers are landed on. Encourage the application of number facts, particularly the use of reversibility from multiplication facts, such as, “Five threes are fifteen. One more three is eighteen so the possum takes six jumps.”

Record the results as equations and diagrams on the empty number line: 

18 ÷ 6 = 3 and 18 – 6 – 6 – 6 = 0

Other examples might be: Three animals on thirty, one takes three-space jumps, one takes five-jumps, one takes six-space jumps.

Four animals on thirty-six, one takes three-space jumps, one takes four-space jumps, one takes five-space jumps, and one takes six-space jumps.

Using Number Properties

Provide students with examples that involve just the equations, such as:

15 ÷ 3 =              16 ÷ 4 =               45 ÷ 5 =                    70 ÷ 10 =

35 ÷ 7 =              48 ÷ 8 =               42 ÷ 6 =                     28 ÷ 4 =

27 ÷ 3 =              32 ÷ 8 = 

Ask the students to provide a story for each equation.