Forming factors

Purpose

The purpose of this activity is to support students in recognising multiplication as an efficient way to combine equal sets.

Achievement Objectives
NA2-1: Use simple additive strategies with whole numbers and fractions.
Required Resource Materials
  • Pictures of eggs and other real, contextually relevant objects in arrays (see PowerPoint) or real cardboard trays and items to act as eggs or fruit, such as counters, small balls, or cubes.
  • Calculators
Activity
  1. Use slide one of the PowerPoint, either displayed on a screen or printed to A3, to pose problems that involve arrays of items (such as eggs).
    Mere buys a tray of eggs for her whanau. 
    How many eggs does she buy?
     
  2. Let the students solve the problem using any strategy. 
     
  3. Gather together and discuss the strategies used. 
    How did you work out the number of eggs in Mere’s tray?
    Record the strategies offered by students using mathematical symbols and expressions. For example:
    5 + 5 + 5 + 5 + 5 + 5 = 30
    6 + 6 = 12, 12 + 12 = 24, 24 + 6 = 30
    10 + 10 + 10 = 30
     
  4. Discuss the efficiency of the different strategies.
    Which strategy is the easiest to use? Why? Note that the "easiness" a strategy is related to available knowledge and prior experience.
     
  5. Use an on-screen or very large calculator to demonstrate how a calculator can be used to solve the problem. 
    How many rows does Mere’s tray have? (Students should say “five.” Type 5 on the calculator)
    How many eggs are in each row?  (Students should say “six”. Type x 6 on the calculator.)
    How do I get the answer? (Students should say “You need to press equals.” Type =.) 
    How do we say this equation in words? (Students might give various answers like “Five times six” or “Six multiplied by five”. If they do not have words, tell them.)
     
  6. Use your cursor to click on slide one of the PowerPoint. This animates a 90 degree turn of Mere’s tray. If you have a physical model turn it 90 degrees (a right turn).
    Here’s a different way to look at Mere’s tray. How many eggs are in the tray now?
    Students may agree that the number of eggs is still 30, some are likely to be less certain.
    How many rows does Mere’s tray have when we look at it this way? (Students should say “six.” Type 6 on the calculator)
    How many eggs are in each row?  (Students should say “five”. Type x 5 on the calculator.)
    How do I get the answer? (Students should say “you need to press equals.” Type =.) 
    How do we say this equation in words? (Students might give various answers like “six times five” or “five multiplied by six”. Encourage the use of appropriate mathematical vocabulary - like times, multiplied, of and product - and te reo Māori kupu - like whakarea (times, of, multiply)).
     
  7. Let’s write down the equations we made on the calculator:
    6 x 5 = 30
    5 x 6 = 30
    What do you notice?
    Look for students to recognise that the order of the numbers being multiplied does not change the answer (the commutative property). You might support this understanding by modelling the problem with tens frames.
     
  8. Look at the other examples of trays in PowerPoint One and, as a class, develop contexts for exploring arrays using students’ names. Ask students to find the total number of items in each array. Allow access to a calculator and encourage students to form multiplication equations. Consider grouping students in pairs or small groups with students with different levels of mathematical knowledge and confidence to encourage tuakana-teina. Allow students to express their mathematical thinking in different ways (e.g. written, verbal, drawn diagrams, acting out).
     
  9. Gather together and provide time for groups of students to share their problems, solutions, and mathematical representations. 
    Use equations to record the strategies used. Together, identify, whether the strategies are additive or multiplicative. Read the equations in words.
    Note that Slide Three shows a non-example, as the rows are a combination of four and five apples. Look for students to adjust their strategies to cope with this, such as 2 x 4 + 2 x 5 = 18.

Next steps

  1. Increase the level of abstraction by covering the materials, asking anticipatory questions, and working with more complex facts, such as 6 x 7 or 9 x 3. More complex examples are likely to ‘sell’ the idea of multiplication to students.
  2. Reverse the task. Give students a multiplication fact, such as 4 x 8, and ask them to draw or make the corresponding array with materials. Find ways to work out the product.
Attachments
Arrays.pptx780.89 KB

Printed from https://nzmaths.co.nz/resource/forming-factors at 3:26am on the 29th March 2024