Diagnostic questions
If each lolly kebab has 15 lollies on it, how many lollies will Jemma need to make 15 kebabs?
Answer: 225
What to notice in the student’s response
Does the student use repeated addition, for example, 15 + 15 + 15 + …?
Can they suggest an alternative strategy when asked?
Does the student overgeneralise the use of place value partitioning in addition by combining 10 x 10 = 100 and 5 x 5 = 25 to get 100 + 25 = 125?
Deliberate acts of teaching
Materials
- 20 memo cube squares
Arrays can help students move beyond repeated addition by providing a visual representation of multiplication concepts.
Show the student an array. Turn it sideways and ask the student whether the array has changed. Show the student a simple array, for example, a 3 x 4 array.
Give the student 10 seconds to look at it, then hide it. Ask the student to use counters to make the array and to count how many counters there are.
Area Array Models for Multiplication
Draw a chalk rectangle on the carpet, small enough to be filled by 12–20 memo cube squares. Ask the student to use the squares to find the area of the rectangle. Explore the multiplicative relationship between length, width, and area.
Increase the area of the rectangle to 50–80 squares, making it impractical to fill it with paper squares. Refer the student back to the length, width, and area relationship of the first rectangle. Use chalk lines to identify different arrays within the rectangle. For example, using a 13 x 6 rectangle, mark out the 10 x 6 section of the array and the 3 x 6 section. Tell the student to record the model as a diagram, including known facts.
This activity can be adapted using Digital Learning Objects, sheets of small stickers, or sticky notes on a table top. Encourage students to use the basic facts that they are familiar with and discourage the use of counting strategies.
What to do next if the student is stuck
Check the student’s knowledge of basic multiplication facts. Revisit smaller arrays. Increase the size of the rectangle gradually until its area can no longer be counted quickly. Note that skip-counting does not indicate the understanding of multiplication as an operation.
Initiating home-based activities
Parents can help the student to recognise and solve array problems within their home and community environments, such as working out the number of cars in a car park, buttons on a remote control, windows in large buildings, or bricks in a wall. The student should locate five array problems each night, record them in their homework book, and show how they used multiplication to solve each problem.
Next teaching steps back in the classroom
Explore square units used in geometry and measurement. Use games such as Multiplication Roundabout (Material master 6-6b)(PDF, 170KB) to provide the students with practice in multiplying two-digit numbers by a one-digit number.
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