mafs.3.oa.4.8 supplemental lesson writing equations for two-step word problems

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?