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X Australian Curriculum Year 5 Solve problems involving multiplication of large numbers by one or two digit numbers using efficient mental, written strategies and appropriate digital technologies ACMNA100 Key Ideas It is important to recognise when multiplication is appropriate to use There are many different ways to multiply numbers Activity Process: Learning Intention: Revise learners understanding of multiplication Ask learners to use multiplication to represent one thousand Ask learners to use multiplication to represent ten thousand Ask learners to use multiplication to represent hundred thousand Ask learners to identify the pattern eg zero place holders. Remind learners that the patterns in the place value system make it easier to interpret and operate with numbers Activity Process: Mystery Numbers Learning Intentions: Practice multiplication while identify and using a strategy Replace the empty boxes with values from 1 to 6 to make the problem true. There is no limit to how often a number is used. 7, 8, 9, or 0 cannot be used This question requires the learner to multiply a two digit numbers by a single digit but gives them a choice of what to do The learner has a choice of numbers 1 to 6 The learner might look for a pattern by multiplying the numbers 2 by 4 but realize that the resulting number 8 cannot be used so they continue to guess and check 1000 X 110 X 1005 X 200 10 000 X 1100 X 10050 X 200 Resources FISH Vocabulary Multiply, backwards, rule, inverse, sum, lattice, 100 000 X 11 000 X 100500 X 200 X The easiest way is to multiply by 1 or 2 resulting in 42 X 1 = 42 or 33 X 2 = 66. Challenge learners to come up with other alternatives and discuss. Using the same rules ask learners to create a sum with a three digit answer Another way to display the mystery numbers is in a number sentence. In this case the strategy Is to work backwards using the inverse. Working independently ask learners to complete this number sentence
Activity Process To improve learners recall and fluency with number facts play the game Dice Tables Two learners need three 1 to 6 dot dice, 2 sets of coloured counters Dice tables board as above. The first player rolls the dice and chooses two of the three numbers to multiply to match a number on their Dice tables board, e.g. if the learner rolls 4, 5 and 3 they could make 4 x 5 = 20 or 4 x 3 = 12 or 5 x 3 = 15. They place a counter on the chosen multiple. Learners alternate turns. The aim is to be the first to get 4 counters in a row, column, diagonal or square. Activity Process To improve learners recall and fluency with number facts play the game Multo Prepare 100 flash cards with the multiplication facts 1 x 1 through to 10 x10. Learners are given a 4 x 4 grid in which they must write 16 different numbers. The winner is the first student to get four numbers in a row, column or diagonal. On completion of a row of 4 the winning student calls out “Multo” As each flash card is shown, learners cross off that product from their game boards. Initially the teacher may decide to have the learners read the card aloud and say the answer before they check it off. This is a good way to reinforce prior learning. At the completion of a game the teacher runs through the flash cards already shown and students again say the question and provide the answer. This is a check that the winner does indeed have a “correct” grid. After the game has been played several times students soon discover that this activity differs from “bingo-style” games in that players can increase their chances of winning in several ways. Students work out for themselves, or with a little help from group discussion, that some numbers are “better” than others. Twenty-four is a “good” number because there are four cards which give that product (6 x 4, 4 x 6, 8 x 3, 3 x 8) whereas only one card (5 x 5) will give the answer 25. If students investigate this further they may discover that there are 9 “best” numbers having four chances of being drawn (6, 8, 10, 12, 18, 20, 24, 30, 40). Four numbers have three chances: 4, 9, 16, 36. Learners may decide to use the results of this investigation when choosing the numbers to place in the grid. Some learners place the “best” numbers on the eight squares which occupy diagonals because they say that these squares have three chances of winning, while the other 8 squares have only two chances. http://www.schools.nsw.edu.au/learning/7- 12assessments/naplan/teachstrategies/yr2012/index.php?id=numeracy/nn_nu mb/nn_numb_s2b_12
Activity Process Lattice Multiplication Learning Intention: Learn about different ways to multiply The Lattice Form of Multiplication dates back to the 1200s or before in Europe. It gets its name from the fact that to do the multiplication you fill in a grid which resembles a lattice one might find climbing plants growing on. In lattice multiplication, the partial products are laid out in a lattice and adding along the diagonals gives the answer to the multiplication 28 X 57 As before the numbers are set out on the lattice and the products are written down in their respective diagonal positions. The numbers along the diagonals are added to give the answer. In this example adding along the third diagonal gives 19 which needs 1 to be carried to the diagonal to the left, in other words, 19 hundreds is 10 hundreds + 9 hundreds, then the 10 hundreds is renamed as 1 thousand and the 1 is then written in the thousands column. 183 × 49 = 8967 The addition should begin with the lowest diagonal on the right hand side (the product of the ones from the two numbers). to take account of the increasing place value as you add to the left Digital Resources-Lattice Multiplication https://www.khanacademy.org/math/arithmetic/multiplication- division/lattice_multiplication/v/lattice-multiplication Play this video for the first 2:40 minutes it is an example of lattice multiplication 2 by 2 digits. The rest of the video shows examples which are beyond the scope of the content description for year 5. ‘Solve problems involving multiplication of large numbers by one or two digit numbers ‘. Give learners the opportunity to explore this multiplication method. Use a free worksheet. It gives an example and explains the steps to solving lattice multiplication problems. There are also several practice problems for students to try. http://www.superteacherworksheets.com/lattice/lattice2_TZBMZ.pdfhttp://www.superteacherworksheets.com/lattice/lattice2_TZBMZ.pdf Blank lattices are also available from http://www.mathworksheets4kids.com/lattice-multiplication.html Assessment Option 1. List 2 multiplication equations this picture might describe 450 Option 2. You multiply two numbers and the product is about 40 more than 42 X 63. What number might you have multiplied? As 28 and 57 have two digits each, a lattice is set out with two columns and two rows. The diagonals are drawn in each cell. 28 is written above the lattice with 2 above the first column and 8 above the second. 57 is written to the right of the lattice with 5 along the first row and 7 along the second. The sum along each diagonal is then recorded as shown. 2 8 5 7 1 4 0 1 5 4 6 The digits in the diagonal are then added and the solution is 28 X 57 = 1596 The digits 1, 5, 9 and 6 form the answer to the multiplication. As usual, start adding at the ones in this example a ‘6’ which comes from multiplying 8 ones by 7 ones. If we multiply 183 by 49 the lattice set out will have 3 columns and two rows as 183 has 3 digits. 9 Tens 6 Ones 1 Thousand 5 Hundred
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