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Lesson Opening Ava bought a pack of 50 colored pencils. Her friend, Marisa, gave her 7 more pencils. Write an equation that represents how many pencils Ava has now. Use the letter p to represent how many pencils Ava now has. + = p
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MAFS.3.OA.4.8SUPPLEMENTAL LESSON
Writing equations for two-step word problems
Lesson OpeningAva bought a pack of 50
colored pencils. Her friend, Marisa, gave her 7 more
pencils. Write an equation that represents how
many pencils Ava has now. Use the letter p to represent how
many pencils Ava now has.
Lesson OpeningAva bought a pack of 50
colored pencils. Her friend, Marisa, gave her 7 more
pencils. Write an equation that represents how
many pencils Ava has now. Use the letter p to represent how
many pencils Ava now has.+ = p
Lesson OpeningAva bought a pack of 50
colored pencils. Her friend, Marisa, gave her 7 more
pencils. Write an equation that represents how
many pencils Ava has now. Use the letter p to represent how
many pencils Ava now has.+ = p50 7
Writing Equations for 2-Step Problems
Step 1: Read the entire problem.Step 2: MODEL one sentence (or part) at a time.Step 3: Find the answer.Step 4: Write an expression for how you solved each part.Step 5: Use a letter for the unknown in the problem.
Writing Equations for 2-Step Problems
Pete has 5 books. Sam has twice as many books as Pete. How many books do they have together?
Writing Equations for 2-Step Problems
Pete has 5 books. Sam has twice as many books as Pete. How many books do they have together?
Step 1: Read the entire problem.
Writing Equations for 2-Step Problems
Pete has 5 books. Sam has twice as many books as Pete. How many books do they have together?
Step 2: Model the problem one sentence at a time.
Writing Equations for 2-Step Problems
Pete has 5 books. Sam has twice as many books as Pete. How many books do they have together?
Step 2: Model the problem one sentence at a time.
Pete
Writing Equations for 2-Step Problems
Pete has 5 books. Sam has twice as many books as Pete. How many books do they have together?
Step 2: Model the problem one sentence at a time.
PetePete
Pete
Sam
Writing Equations for 2-Step Problems
Pete has 5 books. Sam has twice as many books as Pete. How many books do they have together?
Step 2: Model the problem one sentence at a time.
PetePete
Pete
Sam1
24
35 6
78
910
1112
14
1315
Writing Equations for 2-Step Problems
Pete has 5 books. Sam has twice as many books as Pete. How many books do they have together?
Step 3: Find the answer.
PetePete
Pete
Sam1
24
35 6
78
910
1112
14
1315They have 15 books
altogether.
Writing Equations for 2-Step Problems
Pete has 5 books. Sam has twice as many books as Pete. How many books do they have together?
Step 4: Write an expression for how you solved each part.
PetePete
Pete
Sam1
24
35 6
78
910
1112
14
13155
Writing Equations for 2-Step Problems
Pete has 5 books. Sam has twice as many books as Pete. How many books do they have together?
Step 4: Write an expression for how you solved each part.
PetePete
Pete
Sam1
24
35 6
78
910
1112
14
13155 + (2 x 5)
Writing Equations for 2-Step Problems
Pete has 5 books. Sam has twice as many books as Pete. How many books do they have together?
Step 5: Use a letter for the unknown in the equation.
PetePete
Pete
Sam1
24
35 6
78
910
1112
14
13155 + (2 x 5) = b
Use a letter for the unknown
Writing Equations for 2-Step Problems
Pete has 5 books. Sam has twice as many books as Pete. How many books do they have together?
The reason there are parentheses around 2 x 5 is because you perform the operation in
parentheses before you can add it to the 5.
5 + (2 x 5) = bUse a letter for the unknown
LET’S TRY ANOTHER ONE…
Writing Equations for 2-Step Problems
Step 1: Read the entire problem.Step 2: MODEL one sentence (or part) at a time.Step 3: Find the answer.Step 4: Write an expression for how you solved each part.Step 5: Use a letter for the unknown in the problem.
Writing Equations for 2-Step ProblemsTom has a box of 18 chocolates. He eats 6
of them and places the rest of them equally into three bags for his sisters. How many chocolates are in each bag?
Writing Equations for 2-Step ProblemsTom has a box of 18 chocolates. He eats 6
of them and places the rest of them equally into three bags for his sisters. How many chocolates are in each bag?
Step 1: Read the entire problem.
Writing Equations for 2-Step ProblemsTom has a box of 18 chocolates. He eats 6
of them and places the rest of them equally into three bags for his sisters. How many chocolates are in each bag?
Step 2: Model the problem one sentence at a time.
Writing Equations for 2-Step ProblemsTom has a box of 18 chocolates. He eats 6
of them and places the rest of them equally into three bags for his sisters. How many chocolates are in each bag?
Step 2: Model the problem one sentence at a time.
Writing Equations for 2-Step ProblemsTom has a box of 18 chocolates. He eats 6
of them and places the rest of them equally into three bags for his sisters. How many chocolates are in each bag?
Step 2: Model the problem one sentence at a time.
Writing Equations for 2-Step ProblemsTom has a box of 18 chocolates. He eats 6
of them and places the rest of them equally into three bags for his sisters. How many chocolates are in each bag?
Step 2: Model the problem one sentence at a time.
Writing Equations for 2-Step ProblemsTom has a box of 18 chocolates. He eats 6
of them and places the rest of them equally into three bags for his sisters. How many chocolates are in each bag?
Step 2: Model the problem one sentence at a time.
Writing Equations for 2-Step ProblemsTom has a box of 18 chocolates. He eats 6
of them and places the rest of them equally into three bags for his sisters. How many chocolates are in each bag?
Step 2: Model the problem one sentence at a time.
Writing Equations for 2-Step ProblemsTom has a box of 18 chocolates. He eats 6
of them and places the rest of them equally into three bags for his sisters. How many chocolates are in each bag?
Step 2: Model the problem one sentence at a time.
Writing Equations for 2-Step ProblemsTom has a box of 18 chocolates. He eats 6
of them and places the rest of them equally into three bags for his sisters. How many chocolates are in each bag?
Step 3: Find the answer.
There are 4 chocolates in each bag.
Writing Equations for 2-Step ProblemsTom has a box of 18 chocolates. He eats 6
of them and places the rest of them equally into three bags for his sisters. How many chocolates are in each bag?
Step 4: Write an expression for how you solved each part.
Writing Equations for 2-Step ProblemsTom has a box of 18 chocolates. He eats 6
of them and places the rest of them equally into three bags for his sisters. How many chocolates are in each bag?
Step 4: Write an expression for how you solved each part.
18
Writing Equations for 2-Step ProblemsTom has a box of 18 chocolates. He eats 6
of them and places the rest of them equally into three bags for his sisters. How many chocolates are in each bag?
Step 4: Write an expression for how you solved each part.
18 – 6
Writing Equations for 2-Step ProblemsTom has a box of 18 chocolates. He eats 6
of them and places the rest of them equally into three bags for his sisters. How many chocolates are in each bag?
Step 4: Write an expression for how you solved each part.
(18 – 6) ÷ 3
Writing Equations for 2-Step ProblemsTom has a box of 18 chocolates. He eats 6
of them and places the rest of them equally into three bags for his sisters. How many chocolates are in each bag?
Step 4: Write an expression for how you solved each part.
(18 – 6) ÷ 3
Writing Equations for 2-Step ProblemsTom has a box of 18 chocolates. He eats 6
of them and places the rest of them equally into three bags for his sisters. How many chocolates are in each bag?
Step 4: Write an expression for how you solved each part.
(18 – 6) ÷ 3
Writing Equations for 2-Step ProblemsTom has a box of 18 chocolates. He eats 6
of them and places the rest of them equally into three bags for his sisters. How many chocolates are in each bag?
Step 4: Write an expression for how you solved each part.
(18 – 6) ÷ 3
Writing Equations for 2-Step ProblemsTom has a box of 18 chocolates. He eats 6
of them and places the rest of them equally into three bags for his sisters. How many chocolates are in each bag?
Step 5: Use a letter for the unknown in the problem.
(18 – 6) ÷ 3 = c
Writing Equations for 2-Step ProblemsTom has a box of 18 chocolates. He eats 6
of them and places the rest of them equally into three bags for his sisters. How many chocolates are in each bag?
Step 5: Use a letter for the unknown in the problem.
(18 – 6) ÷ 3 = cUse parentheses around
what you have to do first.
ONE MORE...
Writing Equations for 2-Step Problems
Step 1: Read the entire problem.Step 2: MODEL one sentence (or part) at a time.Step 3: Find the answer.Step 4: Write an expression for how you solved each part.Step 5: Use a letter for the unknown in the problem.
Writing Equations for 2-Step Problems
Ms. Percy bought 4 boxes of paperclips. She gave 11 of the paperclips away to her
students. Then she had 13 paperclips left. How many paperclips were in each box?
Writing Equations for 2-Step Problems
Ms. Percy bought 4 boxes of paperclips. She gave 11 of the paperclips away to her
students. Then she had 13 paperclips left. How many paperclips were in each box?
Step 1: Read the entire problem.
Writing Equations for 2-Step Problems
Ms. Percy bought 4 boxes of paperclips. She gave 11 of the paperclips away to her
students. Then she had 13 paperclips left. How many paperclips were in each box?
Step 2: Model the problem one sentence at a time.
Writing Equations for 2-Step Problems
Ms. Percy bought 4 boxes of paperclips. She gave 11 of the paperclips away to her
students. Then she had 13 paperclips left. How many paperclips were in each box?
Step 2: Model the problem one sentence at a time.
Writing Equations for 2-Step Problems
Ms. Percy bought 4 boxes of paperclips. She gave 11 of the paperclips away to her
students. Then she had 13 paperclips left. How many paperclips were in each box?
Step 2: Model the problem one sentence at a time.
Writing Equations for 2-Step Problems
Ms. Percy bought 4 boxes of paperclips. She gave 11 of the paperclips away to her
students. Then she had 13 paperclips left. How many paperclips were in each box?
Step 2: Model the problem one sentence at a time.
?
Writing Equations for 2-Step Problems
Ms. Percy bought 4 boxes of paperclips. She gave 11 of the paperclips away to her
students. Then she had 13 paperclips left. How many paperclips were in each box?
Step 3: Find the answer.
?Let’s work
backwards. If I have 13 now and I just gave away 11, how many
paperclips did I start with?
Writing Equations for 2-Step Problems
Ms. Percy bought 4 boxes of paperclips. She gave 11 of the paperclips away to her
students. Then she had 13 paperclips left. How many paperclips were in each box?
Step 3: Find the answer.
?Let’s work
backwards. If I have 13 now and I just gave away 11, how many
paperclips did I start with?
1311
Writing Equations for 2-Step Problems
Ms. Percy bought 4 boxes of paperclips. She gave 11 of the paperclips away to her
students. Then she had 13 paperclips left. How many paperclips were in each box?
Step 3: Find the answer.
?Let’s work
backwards. If I have 13 now and I just gave away 11, how many
paperclips did I start with?
1311 +
Writing Equations for 2-Step Problems
Ms. Percy bought 4 boxes of paperclips. She gave 11 of the paperclips away to her
students. Then she had 13 paperclips left. How many paperclips were in each box?
Step 3: Find the answer.
?Let’s work
backwards. If I have 13 now and I just gave away 11, how many
paperclips did I start with?
13 11 +
= 24
Writing Equations for 2-Step Problems
Ms. Percy bought 4 boxes of paperclips. She gave 11 of the paperclips away to her
students. Then she had 13 paperclips left. How many paperclips were in each box?
Step 3: Find the answer.
?Let’s work
backwards. 24 paperclips were in 4 boxes. So many were in 1
box?
24
Writing Equations for 2-Step Problems
Ms. Percy bought 4 boxes of paperclips. She gave 11 of the paperclips away to her
students. Then she had 13 paperclips left. How many paperclips were in each box?
Step 3: Find the answer.
6Let’s work
backwards. 24 paperclips were in 4 boxes. So many were in 1
box?
=24
666
Writing Equations for 2-Step Problems
Ms. Percy bought 4 boxes of paperclips. She gave 11 of the paperclips away to her
students. Then she had 13 paperclips left. How many paperclips were in each box?
Step 3: Find the answer.
6There were 6 paperclips in
each box.
=24
666
Writing Equations for 2-Step Problems
Ms. Percy bought 4 boxes of paperclips. She gave 11 of the paperclips away to her
students. Then she had 13 paperclips left. How many paperclips were in each box?
Step 4: Write an expression for how you solved each part.
Now, write the equation based on how you solved the
problem.
Writing Equations for 2-Step Problems
Ms. Percy bought 4 boxes of paperclips. She gave 11 of the paperclips away to her
students. Then she had 13 paperclips left. How many paperclips were in each box?
Step 4: Write an expression for how you solved each part.
13 + 11
Writing Equations for 2-Step Problems
Ms. Percy bought 4 boxes of paperclips. She gave 11 of the paperclips away to her
students. Then she had 13 paperclips left. How many paperclips were in each box?
Step 4: Write an expression for how you solved each part.
(13 + 11) ÷ 4
Writing Equations for 2-Step Problems
Ms. Percy bought 4 boxes of paperclips. She gave 11 of the paperclips away to her
students. Then she had 13 paperclips left. How many paperclips were in each box?
Step 5: Use a letter for the unknown in the problem.
(13 + 11) ÷ 4 = p
Your TurnStep 1: Read the entire problem.
Step 2: MODEL one sentence (or part)
at a time.
Step 3: Find the answer.
Step 4: Write an expression for how you solved each part.
Step 5: Use a letter for the unknown in the problem.
Pedro has 24 toy cars in his bedroom. He has
the cars equally divided into 3 boxes. If he
gives 1 box away to his brother, how many toy cars does Pedro have
left?(24 ÷ 3) – 8 = c
c = 16
Your TurnStep 1: Read the entire problem.
Step 2: MODEL one sentence (or part)
at a time.
Step 3: Find the answer.
Step 4: Write an expression for how you solved each part.
Step 5: Use a letter for the unknown in the problem.
Ms. Bellas makes 32 cupcakes for her
students. But before she could bring them to
school her family ate 8 cupcakes. She packed
the rest of the cupcakes equally into 3 containers. How many cupcakes are
in each container?(32 – 8) ÷ 3 = cc = 8
Your TurnStep 1: Read the entire problem.
Step 2: MODEL one sentence (or part)
at a time.
Step 3: Find the answer.
Step 4: Write an expression for how you solved each part.
Step 5: Use a letter for the unknown in the problem.
At a restaurant each adult meal costs $12 and kids eat free. If a group of
14 people went to eat and 6 were kids, how much would it cost for
the whole group to eat?
(14 – 6) × 12 = dd = 96
Your Turn
Solve each problem. Match the problem to
the equation that could be used to solve the problem.
Exit TicketWrite an equation with a letter representing the
unknown for the following situation. Then solve for the letter.
A painter needed to paint 26 rooms in a building. Each room takes 9 hours to paint. If she
already painted 17 rooms, how many more hours will it take
her to paint the rest?