Download NS5-23 - JUMP Math

WORKBOOK 5:1
PAGE 67
NS5-23
Mental Math
ASK: How can we use an array to show 3 × 12? Have a volunteer draw it on
GOALS
Students will multiply large
numbers by breaking them
into smaller numbers.
PRIOR KNOWLEDGE
REQUIRED
Multiplication
Arrays
Distributive property
Commutative property
of multiplication
the board. Then ask if anyone sees a way to split the array into two smaller
rectangular arrays, as in the last lesson. Which number should be split—the
3 or the 12? SAY: Let’s split 12 because 3 is already small enough. Let’s
write: 12 =
+
. What’s a nice round number that is easy to multiply
by 3? (10) Fill in the blanks (12 = 10 + 2) then have a volunteer split the
array. ASK: What is 3 × 10? What is 3 × 2? What is 3 × 12? How did you
get 3 × 12 from 3 × 10 and 3 × 2? Have a volunteer write the math sentence
that shows this on the board: 3 × 12 = 3 × 10 + 3 × 2.
ASK: Did we need to draw the arrays to know how to split the number 12
apart? Ask students to split the following products in their notebooks without
drawing arrays (they should split the larger number into two smaller numbers,
one of which is a multiple of 10):
a) 2 × 24
b) 3 × 13
c) 4 × 12
d) 6 × 21
e) 9 × 31
f) 4 × 22
When students are comfortable splitting these products into the sum of
two smaller products, have them solve each problem.
Give early finishers these slightly more difficult problems:
a) 2 × 27
b) 3 × 14
c) 7 × 15
d) 6 × 33
e) 8 × 16
To solve these products, students will have to do more than just copy
digits when adding the numbers in the last step (EXAMPLE: 2 × 27 =
2 × 20 + 2 × 7 = 40 + 14 = 54).
ASK: To find 2 × 324, how can we split the 324 into smaller numbers that are
easy to multiply by 2? How would we split 24 if we wanted 2 × 24? We split
24 into 2 tens and 4 ones. What should we split 324 into?
324 = 300 + 20 + 4, SO:
2 × 324
=
2 × 300 + 2 × 20 + 2 × 4
Have students multiply more 3-digit numbers by 1-digit numbers by
expanding the larger number and applying the distributive property.
(EXAMPLES: 4 × 231, 8 × 126, 5 × 301)
WORKBOOK 5
Part 1
Number Sense
Copyright © 2007, JUMP Math
Sample use only - not for sale
59
WORKBOOK 5:1
PAGE 67
Students should record their answers and the corresponding base ten models in their notebooks.
Then have them solve additional problems without drawing models. Finally, have them solve
problems in their heads.
Bonus
Students who finish quickly can do problems with 4- and 5-digit numbers.
Extensions
1. Have students draw models for 2 × 24 and 24 × 2. How would they split the two rectangles?
Emphasize that just as 2 × 24 = 2 × 20 + 2 × 4, we can split 24 × 2 as follows: 24 × 2 =
20 × 2 + 4 × 2. Have students multiply 2-digit numbers by 1-digit numbers, as they did during
the lesson, but with the larger number first (EXAMPLES: 13 × 3, 12 × 4, 21 × 6).
2. Have students combine what they learned in this lesson with what they learned in lesson
NS5-21. Ask them to multiply 3-digit numbers by multiples of 1000 or 10 000.
a) 342 × 2000
b) 320 × 6000
c) 324 × 2000
d) 623 × 20 000
3. Have students calculate the total number of days in a non-leap year:
a) By adding the sequence of 12 numbers:
31 + 28 + 31 + … + 30 + 31 =
b) By changing numbers to make a multiplication and addition statement:
31 + 28 + 31 +
30 + 1 30 – 2 30 + 1
30
30
+
31 +
30 + 1
30
30
+
31 +
30 + 1
…
+
31
30 + 1
= 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30 + 30
+1+1+1+1+1+1+1–2
= 30 × 12 + 5 = 360 + 5 = 365.
Guide the students by asking what a good round number is that is close to 28 and 31 that they
can change all 12 numbers to. Then have them think about how to adjust for the changes they
made. If they pretend all the numbers are 30, how many times would they have to add 1 to get
the actual number of days? (7) How many times would they have to subtract? (only once for
February) What are they subtracting by? (2) What is the overall effect? (adding 5)
60
Copyright © 2007, JUMP Math
Sample use only - not for sale
TEACHER’S GUIDE
NS5-23: Mental Math
page 67
4 × 23
To multiply 4 × 23, Anya rewrites 23 as a sum:
23 = 20 + 3
She multiplies 20 by 4:
4 × 20 = 80
Then she multiplies 4 × 3:
4 × 3 = 12
Finally she adds the result:
80 + 12 = 92
The picture shows why Anya’s method works:
4 × 3 = 12
4 × 20 = 80
4 × 23 = 4 × 20 + 4 × 3 = 80 + 12 = 92
1. Use the picture to write the multiplication statement as a sum. The first one is started for you:
a)
2 × 20
4 × 14
b)
2 × 23
+
2×
2. Multiply using Anya’s method. The first one has been done for you:
4 × 10 + __________
4 × 2
40 + 8 = ________________
48
a) 4 × 12 = __________
= __________
b) 3 × 43 = __________ + __________ = __________ = ________________
c) 4 × 22 = __________ + __________ = __________ = ________________
3 × 200
3 × 30
3 × 1
600 + 90 + 3
693
d) 3 × 231 = __________
+ __________
+ __________
= ________________
= _________
e) 2 × 443 = __________ + __________ + __________ = ________________ = _________
f)
3 × 313 = __________ + __________ + __________ = ________________ = _________
3. Multiply in your head by multiplying the digits separately.
a) 2 × 12 = ______
b) 2 × 42 = ______
c) 3 × 12 = ______
d) 4 × 11 = ______
e) 4 × 21 = ______
f) 3 × 41 = ______
g) 2 × 32 = ______
h) 3 × 23 = ______
2 × 233 = ______
k) 3 × 232 = ______
l)
n) 2 × 442 = ______
o) 4 × 212 = ______
p) 3 × 333 = ______
i)
3 × 112 = ______
m) 3 × 132 = ______
j)
4 × 222 = ______
4. a) Atilla planted 332 trees in each of 3 rows.
How many trees did he plant altogether?
b) Rema put 320 nails in each of 3 boxes.
How many nails did she put in the boxes?
Number Sense 1