![]() Measurement quantities, especially time, are more intangible than ‘bags of’ or ‘packets of’ in equal sets situations. It is good if students notice that the situations are structurally similar to the ‘equal sets’ problems from the previous session. Draw on the multiplicative strategies students used previoulsy, and model how to work out the answer when necessary. On the first day, work through several measurement rate problems.Some students may solve these problems without equipment, using the number knowledge they have available. It is important that students are provided with opportunities to build up multiplication facts to 10 and then to 20. They think about the most efficient ways of solving the problems. They are encouraged to model the problems using different equipment and explain their answers to others. Over the next three days the students are exposed to a variety of different types of story problems. Expect that the strategies used by individual students will vary. 5 x 3 = 15 so 6 x 3 = 18 (3 more)?īe aware that students’ choice of strategy depends on the connection between the conditions of each problem and the number resources that they have available. Do they apply multiplication facts, e.g.Do they try to count the contents of each ice-cream container by ones that is, those that are visible and those that are concealed?.What strategy do the students use to solve the problems?.Ask the students to write story problems for each example. Use several sets of ice-cream containers (all with the same number of items in them) with the contents of each covered except for one.For example, “Write a multiplication problem with an answer of 24”. Now ask the students to make up word problems using the problem structure above with different answers.For example, 7 x 4 = 20 means seven sets of four. The multiplication symbols can be thought of as meaning ‘of’. Discuss what the numbers 4, 7, and 28 refer to and what the operations symbols + and x refer to. Note: It is important to link the examples (where possible) to the structure of repeated addition of equivalent sets as multiplication. drawing a picture to show the number of waka and the corresponding number of students.The students can represent these and similar ‘equal sets’ problems with: Also consider how students might benefit from working in pairs (tuakana-teina). When writing these problems, consider what times tables your students are confident in applying to word problems. There are 7 waka in the race. Each waka holds 3 students.There are 6 bags of shellfish (kaimoana).Each one can take 2 people on the school trip. Introduce the session by asking the students to work through several equal group (set) problems first and then ask them to pose their own problems.Using a variety of materials can help students see the multiplicative structure that is common to a variety of problems and assist them to transfer their understanding to situations which are new to them. In other words, the order of the factors does not affect the product (answer) in multiplication.Īs well as thinking about multiplication in a variety of situations, students are encouraged to use a variety of materials to solve the problems. For example, this chocolate block has two rows of five pieces (2 x 5 or 5 x 2).Īrray problems can help students to see the commutative property of multiplication, for example, that 5 x 2 = 2 x 5. An array is a structure of rows and columns. A multiplicative answer is 4 x 3 =12 so Anshul’s block is four times higher than Min’s. How much taller is Anshul’s block than Min’s?”Īn additive answer is 12 – 3 = 9 floors. Comparison problems involve the relationship between two quantities, for example: The rate in Hone’s problem is “five centimetres for every week". How long will his plant be after six weeks?” “Hone’s kumara plant grows five centimetres each week after it sprouts. A measurement rate problem is usually something like this: This is an equal sets problem that contains the rate "four biscuits for every bag". How many biscuits does she buy altogether?” All multiplication situations contain some form of rate but at this level, the problems are usually about equal sets or measurement. They do so by solving rate problems, comparison problems and array problems.Ī rate problem involves a statement of "so many of one quantity for so many of another quantity". ![]() ![]() In this unit, students think about multiplication as a short way to find the result of repeated addition of equal sets. Multiplication is used in many different situations. The basic concept of multiplication is an important one because of its practicality (how much do 4 ice creams cost at $2 each?) and efficiency (it is quicker to determine 4 x 2 than to calculate 2 + 2 + 2 + 2).
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