Download Solving problems with all operations

M4.A.2 Understand the
meanings of operations, use
operations and understand
how they relate to each other.
M4.A.2.1 Use operations to solve
problems (may include word
problems).
M4.A.2.1 Eligible Content
• M4.A.2.1.1 Solve problems involving all
operations with whole numbers, and/or explain
the solution (limit to two-step problems; e.g.,
multiply then add – single digit multipliers and
divisors).
• M4.A.2.1.2 Solve problems involving addition or
subtraction with decimals through the tenths or
money to the cent and/or explain the solution.
Limit to two-step problems.
M4.A.2.1.1 Solve problems
involving all operations with
whole numbers, and/or explain
the solution (limit to two-step
problems; e.g., multiply then add
– single digit multipliers and
divisors).
PSSA Sample Item
PSSA Sample Item
PSSA Sample Item
PSSA Sample Item
PSSA Sample Item
Addition
• To add 723 and 246,
first we add three
six
and _______.
• To add 723 and 246, next we add two and
_______.
four
• To add 723 and 246, next we add seven and
_______.
two
Subtracting
• Can we take one away from zero? No
• To find the difference between 805 and 215,
regroup
next we _______
one hundred as ten tens.
• To find the difference between 805 and 215,
one
next we take _______
away from ten.
• To find the difference between 805 and 215, next
we take _______
away from seven.
two
Multiplication
• To solve 21 × 42, first
we multiply the top
number by the bottom
number's _______
Ones
value.
• What is 2 × 2?
4
• Next, we multiply the top number by the bottom
tens
number's _______
value.
• As we are multiplying by the _______
tens value, we
must first place a zero to keep the place values
lined up correctly.
• When multiplying two two-digit numbers,
product
we write the second _______
below the
first. We must make sure we line up the
place values.
• What is 4 × 1?
4
• What is 4 × 2?
8
products
• Finally, we must add the _______.
Division
• To divide a two-digit number by a one-digit
number, we must write the two-digit
Right
number to the _______
of the one-digit
number.
• What is a dividend?
A number to be divided
• What is a divisor
A number that a dividend
will be divided by.
• What is a quotient?
The result of a
division sentence
• What is a remainder?
An amount left over
after dividing two numbers.
• First, we divide the dividend's tens value by the
_______.
Divisor
• What is 6 ÷ 4?
• 1 with a remainder
• What is the first digit
of the quotient?
• 1
• After dividing the dividend's tens value by the
multiply
divisor, we _______
the divisor by the quotient's
tens value.
• What is 4 × 1?
•4
• After multiplying the
divisor by the
quotient's tens value,
we _______
subtract four from
six.
• After subtracting four
from six, we bring
down the dividend's
_______
value.
ones
• After bringing down
the dividend's ones
value, we divide 20 by
the _______.
divisor
• What is 20 ÷ 4?
•5
• After we divide 20 by the
multiply the
divisor, we _______
divisor by the quotient's
ones value.
• What is 4 × 5?
• 20
• After multiplying the
divisor by the
quotient's ones value,
we _______
20 from
subtract
20.
• What is 20 - 20?
•0
• This quotient has no
_______.
Remainder
Solving Word Problems
Step 1
UNDERSTAND the problem.
What are you trying to figure out?
Here’s an example:
Yesterday, Alex saw 14 birds in his
backyard. Today, he saw 12. How many
birds did he see in all?
In this problem, what are you trying to figure
out?
If you said:
“How many birds did Alex see in all?”
then…
You’re right!
Step 2
Get a PLAN.
How will you answer the question?
Should you ADD or SUBTRACT?
Look for clues.
Here are some
CLUE WORDS
that will help you
decide what to
do.
Addition Clue
Words
in all
altogether
sum
total
Subtraction Clue
Words
how many more
how many are left
difference
Let’s look at the
example again.
Yesterday, Alex saw 14 birds in his
backyard. Today, he saw 12. How many
birds did he see in all?
Do you see any CLUE WORDS?
If you said…
“in all,” then…
You’re right!
The words “in all” tell us that we should
ADD!
Now that we UNDERSTAND the problem,
and have a PLAN, we’re ready for the next
step!
Step 3
SOLVE it!
Write a number sentence using the
information in the problem, and…
Work it out!
Give it a try!
Yesterday, Alex saw 14 birds in his
backyard. Today, he saw 12. How many
birds did he see in all?
Write a number sentence and SOLVE it.
If you wrote…
14 + 12 = 26 then…
You’re right!
Step 4
LOOK BACK.
Does your answer fit the question?
We had to find out how many birds Alex saw
in all.
We added the number he saw yesterday
and the number he saw today.
Our answer was “Alex saw 26 birds in
all.”
It makes sense!
Here are the steps
once more:
Step 1 – UNDERSTAND the
problem.
Step 2 – Get a PLAN.
Step 3 – SOLVE it!
Step 4 – LOOK BACK.
Practice Word Problems
1. There are 11 crows perched on the branch of a tree. How
many feet are there on the branch?
• 11 x 2 = 22 feet
2. A starfish has 5 arms. How many arms do 6 starfish have?
• 5 x 6 = 30 arms
3. There are 3 butterflies. Each butterfly has 4 black dots and
10 yellow dots. How many black dots are there in all?
• 3 x 4 = 12 black dots
4. There are 2 lions and 5 tigers in a circus show. How many legs
are there in all?
• 5 + 2 = 7 4 legged animals
7 x 4= 28 legs
5. A magician has 6 hens. He makes each hen lay 5 eggs. How
many eggs are there in all?
• 6 x 5 = 30 eggs
1. There are 3 cakes. Each cake is cut into 7 parts. Each part is further cut
into 3 pieces. How many cake pieces are there in all?
• 3 x 7 = 21
21x 3 = 63 There are 63 pieces of cake in all.
2. The Professors at the State University drank 58 cups of tea yesterday.
They drank 24 cups in the morning and 13 in the afternoon. How many did
they drink in the evening?
• 58-24= 34 cups left after the morning, 34-13= 21 cups left after the
afternoon which leaves 21 cups of tea left to drink in the evening.
3. Brian borrowed 10 books from the school library. He returned 4 books
yesterday and 4 books today. How many books does he still have?
• 10- 4 = 6 books left after yesterday. 6-4= 2 books left after today. Which
means he has 2 books left.
4. For her new kitchen, Mrs. Barbara bought a crockery set, a cutlery set and
a pressure cooker. Each item cost $ 33 . How many dollars did she spend?
• $33.00 x 3 items = $99.00 dollars.
5. There are 2 paintings on each of three walls of a room. If an art gallery has 5
such rooms, how many paintings are there in its collection?
• 2 x 3= 6 paintings per room. 6 x 5= 30 paintings in the collection.
M4.A.2.1.2 Solve problems
involving addition or subtraction
with decimals through the tenths
or money to the cent and/or
explain the solution. Limit to twostep problems.
PSSA Sample Item
PSSA Sample Item
Essential Question:
•
•
•
•
How do I add and subtract decimals?
Always line up decimals
Add and subtract like you always do
Bring decimal straight down in your
answers
Adding
Examples:
4.55 + 11.3
Put the first number on
the top of the second
number and line up the
decimals.
You can
add a zero
to help
4.55
keep
+ 11.30
everything
lined up
15.85
When adding
or subtracting
you always
start from the
right and work
left.
6.44 + 16
When there is
not a decimal
put one
behind the
number.
Line up
the
decimal
6.44
+ 16.0
22.44
Add a
zero to
line up
everythin
g
Subtracting
Examples:
5.34 -2.08
Put the first number on
the top of the second
number and line up the
decimals.
5.34
-2.08
3.26
Different signs
Take difference
28 – 15.911
When there
is
not a decimal
put one
behind the
number.
7 99
28. 000
-15.911
1 2.0 8 9
Add zeros to
line up
everything,
then
subtract
• What is 0.159 + 2.12?
• Regrouping in
addition, also known
Carrying
as _______,
is putting
a number from the
tens place of a
column answer into
the next higher place
value to the left.
• What is 0.90 + 0.10?
• Regrouping in subtraction, also known as
borrowing is taking 1 from a column and
_______,
adding it as a unit of 10 to the column to the
right.
• What is 0.80 - 0.51?
• What is 4.35 - 2.27?
Adding and Subtracting Decimals
When adding & subtracting numbers with
decimals, stack the numbers on top of each
other lining the decimals up. Remember, if
a number doesn’t have a decimal, it comes
at the end of the number.
EX: 5.2 + 97.44  97.4
+ 5.2
I can fill in empty spots with zeros. When I
subtract, I have to fill in empty spots with
0’s. It’s not necessary with addition.
• 722.8 + 0.2 
722.8
+ 0.2
723.0
ON ADDITION, you don’t have to fill in 0’s
but you can.
With SUBTRACTION, you need to fill in 0’s if
the number is on top. EX: 8 – 2.54
8.0
- 2.5
5.5
•
75 – 0.24 
-
75
0.2
(add a decimal
& a couple 0’s)
75.0
- 0.2
74.8
Now try these:
a) 10.4 - 0.2
c) 342.7 – 3.8
b) 100.3 – 20.4
d) 43 – 7.2
Now try these:
a) 10.4 - 0.2
c) 342.7 – 3.8
b) 100.3 – 20.4
d) 43 – 7.2
First: line up the decimals
10.4
100.3 342.7
43.0
-0.2
-20.4
- 3.8
-7.2
10.2
79.9 338.9
35.8
•
•
•
•
•
72.3 – 4
89 – 42.3
44.2 – 39.6
66.2 – 44.9
Line up the decimals as shown below
• These will all need 0’s added.
• 72.3
89.0 44.2
66.2
- 4.0 -42.3 -39.6
-44.9
• These will all need 0’s added.
• 72.3
89.0 44.2
66.2
- 4.0 -42.3 -39.6
-44.9
68.3
46.7
4.6
21.3
The veterinarian told Camilla that the mass of
her puppy increased by 3.5 kg in the last
month. If the puppy has a mass of 35.6 kg
now, what was its mass a month ago?
35.6kg
+3.5kg
39.1kg