Download NBT5-33 - JUMP Math

NBT5-33 Mental Math
Pages 78–79
STANDARDS
5.NBT.A.2, preparation for
5.NBT.B.5
Vocabulary
area
length
width
Goals
Students will use mental math to divide multiples of powers of 10 by
single-digit divisors, and use the distributive property to perform mental
math division
PRIOR KNOWLEDGE REQUIRED
Can multiply 1-digit numbers with confidence
Can use base ten blocks to model multiplication
MATERIALS
base ten blocks
Divide with base ten blocks. Ask students to place 6 ones blocks on their
desks. Ask them to divide the blocks into 2 equal sets:
ASK: What is a division equation for this diagram? (6 ÷ 2 = 3)
Ask students to place 6 tens blocks on their desks. Ask them to divide them
into 2 equal sets:
ASK: What is a division equation for this diagram? (60 ÷ 2 = 30)
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Ask students to place 6 hundreds blocks on their desks. Ask them to divide
them into 2 equal sets:
ASK: What is a division equation for this diagram? (600 ÷ 2 = 300)
Write the three division equations on the board:
6÷2=3
60 ÷ 2 = 30
600 ÷ 2 = 300
ASK: What is the difference between these equations? (the number of
zeros) How can we tell what the number of zeros will be? (the number of
zeros in the quotient is the same as the number of zeros in the dividend)
How can we find the non-zero numbers in the quotient? (ignore the zeros
and divide the non-zero numbers in the dividend by the divisor)
Number and Operations in Base Ten 5-33
E-25
Exercises
1. Divide using mental math.
a)8 ÷ 2 =
b)12 ÷ 3 =
c)6 ÷ 3 =
d)14 ÷ 2 =
e)10 ÷ 5 =
, so 80 ÷ 2 =
, so 120 ÷ 3 =
, so 60 ÷ 3 =
, so 140 ÷ 2 =
, so 100 ÷ 5 =
and 800 ÷ 2 =
and 1,200 ÷ 3 =
and 600 ÷ 3 =
and 1,400 ÷ 2 =
and 1,000 ÷ 5 =
Bonus
f)9 ÷ 3 =
g)70 ÷ 7 =
, so 900 ÷ 3 =
, so 7,000 ÷ 7 =
.
.
.
.
.
and 90,000 ÷ 3 =
and 700,000 ÷ 7 =
.
.
Answers: a) 4, 40, 400; b) 4, 40, 400; c) 2, 20, 200; d) 7, 70, 700;
e) 2, 20, 200; Bonus: f) 3, 300, 30,000; g) 10, 1,000, 100,000
Review multiples for mental math. Ask students to write down multiples
of …
a) 10 (10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, …)
b) 20 (20, 40, 60, 80, 100, 120, 140, 160, 180, …)
c) 30 (30, 60, 90, 120, 150, 180, 210, 240, …)
Tell students that sometimes we can use these multiples to help us divide
using mental math.





Review columns and rows. Draw the diagrams in the margin on the board.
Remind students that columns are vertical and rows are horizontal.
ASK: How many dots are there altogether? (15) How many rows are there?
(5) What division equation can we use to find the number of columns?
(15 ÷ 5 = 3)
Draw the diagrams in the margin on the board.
ASK: How many squares are there? (12) What is the length? (4) What
division equation can help us find the width? (12 ÷ 4 = 3)
a)
3
      b) 


4 

?



 
















c)
?
Answers: a) 15 ÷ 3 = 5, b) 20 ÷ 4 = 5, c) 30 ÷ 5 = 6
5
?
Use the distributive property to perform mental math. Write on the
board: 75 ÷ 3 = ?. Tell students that you want to find the dimensions of an
area that is 75 square units. You know that the width measures 3 units.
Tell students that mental division can be made easier by breaking up
numbers such as 75 into two numbers that are easier to divide. One of
the numbers should be a multiple of 10, 20, 30, 40, etc., that we know
is divisible by 3.
E-26
Teacher’s Guide for AP Book 5.1
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Exercises: Write a division equation to help find the missing number.
(Hint: count the total number of dots or squares first.)
We know 15 is a multiple of 3.
In this case: 75 = 60 + 15
We know 60 is a multiple of 3 because 6 is a multiple of 3.
Draw on the board:
3
60
15
3
60
?
3
?
15
?
SAY: So trying to find the length of the rectangle with area 75 square units
and width 3 units can be broken into two parts: finding the length of a
rectangle with area 60 square units and width 3 units, and finding the length
of a rectangle with area 15 square units and width 3 units.
Finding length of
rectangle with area 60
Finding length of
rectangle with area 75
75 ÷ 3
=
=
=
(60) ÷ 3
20
Finding length of
rectangle with area 15
+
+
25
(15) ÷ 3
5
Remind students that 60 ÷ 3 = 20 because 6 ÷ 3 = 2.
For the exercises, provide the hints for those students who have trouble
finding the multiples.
(MP.1, MP.7)
Exercises: Use a multiple of 10, 20, 30, 40, etc., to break down the
dividend and perform the division using mental math.
1.a)70 ÷ 5 (Hint: 70 = 50 + 20)
b) 68 ÷ 4 (Hint: 68 = 40 + 28)
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c)87 ÷ 3 (Hint: 87 = 60 + 27)
2.a)824 ÷ 4 (Hint: 800, 24)
b) 1248 ÷ 6 (Hint: 1200, 48)
c)2456 ÷ 8 (Hint: 2400, 56)
d) 7236 ÷ 9 (Hint: 7200, 36)
Sample Solution
1.a)70 ÷ 5
= (50 ÷ 5) + (20 ÷ 5)
= 10 + 4
= 14
Answers: 1. b) 17, c) 29; 2. a) 206, b) 208, c) 307, d) 804
Number and Operations in Base Ten 5-33
E-27
NBT5-33 Mental Math
REMINDER
ones
tens
hundreds
thousands
1. Divide the blocks into two equal groups. Then write the division equation.
a)
6 ÷ 2 = 3 c)
÷ 2 = b)
60 ÷ 2 = d)
÷ 2 = 2. Divide into equal groups. Then finish the division equation.
a) 8 tens ÷ 4 = 2 tens
So 80 ÷ 4 = 20 b) 12 hundreds ÷ 3 = hundreds
So 1,200 ÷ 3 = c) 6 thousands ÷ 2 = thousands
So 6,000 ÷ 2 = d) 32 thousands ÷ 8 = thousands
So 32,000 ÷ 8 = 3.Divide.
b)20 ÷ 4 = 90 ÷ 3 = 200 ÷ 4 = 900 ÷ 3 = 2,000 ÷ 4 = 9,000 ÷ 3 = 20,000 ÷ 4 = 4.Divide.
a)800 ÷ 2 = b)600 ÷ 3 = c) 12,000 ÷ 4 = d)14,000 ÷ 7 = e)25,000 ÷ 5 = f ) 24,000 ÷ 6 = 78
Number and Operations in Base Ten 5-33
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a)9 ÷ 3 = 5. Write a division statement for each part of the picture. Then complete the equation.
a)
15 ÷ 3 b)
9 ÷ 3 6 ÷ 3 15 ÷ 3 = (9 ÷ 3) + (6 ÷ 3) c)
d)
6. Write an equivalent division statement. Then find the answer.
a)46 = 40 + 6
b) 69 = 60 + 9
So 46 ÷ 2 = (40 ÷ 2) + (6 ÷ 2) So 69 ÷ 3 = = 20 + 3 = 23 c)75 = 60 + 15
d) 120 = 100 + 20
= = e) 72 = 60 + 12
f ) 96 = 80 + 16
These numbers are divisible by 2: 20, 40, 60, 80, 100.
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These numbers are divisible by 3: 30, 60, 90, 120.
7. Find the answer by writing a pair of easier division statements.
a)45 ÷ 3 = (30 ÷ 3) + (15 ÷ 3) b) 75 ÷ 3 = = 10 + 5 = 15 c)72 ÷ 2 d) 81 ÷ 3 = = e) 94 ÷ 2
f ) 92 ÷ 4
8. Divide mentally. Explain how you found the answer to parts a) and d).
a)63 ÷ 3 b) 65 ÷ 5
Number and Operations in Base Ten 5-33
c) 84 ÷ 7
d) 78 ÷ 6 BONUS
126 ÷ 3
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