Transcript Mag_5.S2.39 - The Curriculum Place

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
Resources
• FISH
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
Vocabulary
Multiply, backwards, rule, inverse, sum, lattice,
Activity Process:
Learning Intention: Revise learners understanding of multiplication
Ask learners to use multiplication to represent one thousand
1000 X 1
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
10 X 100
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
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.
5 X 200
Ask learners to use multiplication to represent ten thousand
10 000 X 1
100 X 100
50 X 200
Ask learners to use multiplication to represent hundred thousand
100 000 X 1
1 000 X 100
500 X 200
X
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.
X
Working independently ask learners to
complete this number sentence
Activity Process To improve learners recall and fluency with number facts play
the game Multo
Activity Process To improve learners recall and fluency with number facts play the
game Dice Tables
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/712assessments/naplan/teachstrategies/yr2012/index.php?id=numeracy/nn_nu
mb/nn_numb_s2b_12
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 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 28 and 57 have two digits each,
2
8
a lattice is set out with two
1
4
columns and two rows. The
5
1
Thousand
diagonals are drawn in each cell. 28
0
0
is written above the lattice with 2
above the first column and 8 above
1
5
5 Hundred
the second. 57 is written to the
7
4
6
right of the lattice with 5 along the
first row and 7 along the second.
9 Tens
6 Ones
The sum along each diagonal is
then recorded as shown.
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.
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/multiplicationdivision/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.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?