Solve multiplication problems using skip counting in twos, fives, and tens.
Say the forwards and backwards skip–counting sequences in the range 0–100 for twos, fives, and tens.
Number Framework Stage 4
Transparent coloured counters
Using Materials
Lay down six sets of two counters. Make each set of counters the same colour.
Problem: I am going to put these counters onto a number strip like this. (put the first
two counters onto the strip covering 1 and 2). When I put all of the counters on what
will be the last number I cover?
Let the students try to image the process of counters being moved.
Have students take turns placing a pair of counters on the next numbers. Each time
ask for predictions about the end-point number:
If I put two more counters onto the strip, how many will I have?
When all the counters are placed, point to the counter at the end of each colour break and get the students to say the numbers, “2, 4, 6, 8,…”. To encourage imaging turn the strip over so the numbers are not visible and replace the counters. Point to given counters and ask students to tell you what number would be under the counter.
Record the operation using the symbols 6 × 2 = 12.
Ask predictive questions like, “I have six sets of two. How many counters would I have if I put on/took off a set of two?” Record the result using symbols, 7 x 2 = 14 or 5 x 2 = 10.
Pose similar problems with counters and the number strip such as: Five sets of three (5 x 3) Four sets of four (4 x 4)
Using Imaging
Shielding: Problem: Turn over the number strip so that the numbers are face down. Ask four students to get five counters of one colour and hide them under their hands. Confirm the fiveness of each set by getting students to lift their hands then replace them.
Ask: How many counters have we got altogether under these hands? If I put all of the counters on the number strip what will be the last number I cover?
Let students try to solve the problem through imaging. Focus them on using doubles or skip counting knowledge:
“How many counters are in these two hands altogether? (5 and 5, that’s ten) How many will be in these two? (another ten) How many is that altogether? (ten and ten is twenty)
“How many counters are under these hands? (five) Imagine I put them on the number strip. Here are another five (lifting the hands then replacing them). How many is that so far on the number strip? And another five?”
If necessary, fold back into materials by putting the sets of counters on to the number strip. Record the results using equations, eg. 4 x 5 = 20, or, 5 + 5 + 5 + 5 = 20. Ask the students how many counters there would be if another five were added or takenaway. Encourage them to build on from the previous total rather than counting from one. Pose similar problems using imaging, ensuring the number chosen are accessible for skip counting.
Nine sets of two (9 x 2 = 18) then 8 x 2 = 16 and 10 x 2 = 20
Three sets of four (3 x 4 = 12) then 4 x 4 = 16 and 5 x 4 = 20
Using Number Properties
Students have a good understanding of Counting On when they can use skip counting sequences to solve multiplication problems. Write multiplication equations and discuss what they mean.
For example, 7 x 2 = ? means, “seven sets of two is the same as fourteen.”
Other suitable examples are: 6 × 5 = ? 10 × 2 = ? 5 × 3 = ? 6 × 4 = ?
Independent Activity
Play a game of “Hit the Spot”. Students need counters, a number strip and a 1-6 die. Decide on the spot number. 10, 12, 15, 16, 18, 20, and 24 are good choices as they have many factors. Players take turns to roll the die (say three comes up). If they can make up to the spot number exactly, in sets of that die number (three), they get a point. So in this case four sets of three makes twelve. Students can model the counts with counters if they need to (putting four sets of three on the strip will reach twelve exactly). The student with the most points after five dice rolls wins.