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Operation Comparison Combat

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Warm Up

Comparing Warm-Up: What's the Difference?

Instructions: Think about these questions and be ready to share your ideas!

1. Imagine you have 5 apples and your friend has 2 apples. How would you explain the difference in the number of apples using words?





2. Now, imagine you have 6 cookies and your friend has 3 cookies. How would you explain the relationship between your number of cookies and your friend's number of cookies using words?





3. What's the big difference in how you thought about question 1 versus question 2?

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Lesson Plan

Operation Comparison Combat

Students will solve two-step word problems involving all four operations with whole numbers, use estimation to assess reasonableness, interpret remainders, and represent problems with equations using a letter for the unknown quantity.

Understanding how to solve multi-step problems is a fundamental life skill, from budgeting pocket money to planning a party. This lesson equips students with strategies to break down complex problems and check their work, building confidence in mathematical reasoning.

Audience

4th Grade Students

Time

90 minutes

Approach

Through interactive slides, guided practice, and a collaborative game, students will explore problem-solving strategies.

Prep

Preparation

15 minutes

Step 1

Warm-Up: What's the Difference?

10 minutes

  • Display Comparing Warm-Up.
  • Ask students to discuss the questions in pairs or small groups.
  • Facilitate a brief class discussion on their answers, focusing on the idea of 'more than' (addition) versus 'times as many' (multiplication). (IEP/ELS: Provide sentence starters for discussion like 'I think the difference is...' or 'One way to explain is...').

Step 2

Introduction: Unpacking Problem Combat

15 minutes

  • Use Operation Comparison Combat Slides (Slides 1-4) to introduce the lesson objectives and the concept of comparing with addition vs. multiplication.
  • Use Operation Comparison Combat Slides (Slide 5: Math Detective's Glossary!) to introduce the key vocabulary words.
  • Follow along with Teacher Script: Operation Combat for key talking points and questions.
  • Emphasize identifying keywords in word problems. (IEP/ELS: Highlight keywords on slides and provide a glossary of terms for the new vocabulary words: 'Associative property,' 'Commutative property,' 'Distributive property,' 'Equation,' 'Product,' 'Variable,' as well as 'sum,' 'quotient,' 'difference.').

Step 3

Guided Practice: Two-Step Takedown

20 minutes

  • Continue with Operation Comparison Combat Slides (Slides 6-9) to work through example two-step problems together.
  • Model how to set up equations with a letter for the unknown quantity.
  • Demonstrate estimation strategies and how to interpret remainders. (IEP/ELS: Provide partially completed equations or graphic organizers to help break down problems).

Step 4

Activity: Problem-Solving Practice

20 minutes

  • Divide students into small groups for the Problem-Solving Practice Activity.
  • Provide each group with a few two-step word problems to solve collaboratively.
  • Circulate and offer support, prompting students to explain their reasoning and use estimation. (IEP/ELS: Pair students with stronger peers; provide simpler problems with fewer steps or smaller numbers).

Step 5

Independent Practice: Worksheet Wizards

15 minutes

  • Distribute the Two-Step Trouble Solvers Worksheet for independent practice.
  • Remind students to show their work, use equations, and estimate their answers.
  • Collect worksheets for assessment. (IEP/ELS: Allow use of calculators for estimation, provide a word bank for problem interpretation, or reduce the number of problems).

Step 6

Game: Operation Chain Reaction

15 minutes

  • Play Operation Chain Reaction Game as a class or in teams.
  • This game reinforces problem-solving in a fun, interactive way.
  • The game will involve students solving problems to 'react' or build upon the previous answer. (IEP/ELS: Allow students to work in pre-assigned teams with mixed abilities).

Step 7

Cool Down: Reflect and Connect

5 minutes

  • Conclude with the Reflect and Connect Cool Down.
  • Ask students to reflect on their learning and any remaining questions. (IEP/ELS: Provide a choice of reflection methods, e.g., drawing a picture, writing one word, or using a thumbs up/down scale for understanding).
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Slide Deck

Welcome, Math Warriors!

Today's Mission:

  • Conquer two-step word problems!
  • Understand the power of estimation.
  • Master tricky remainders.
  • Write awesome equations!

Welcome students and introduce the day's challenge: becoming 'Operation Combat' experts! Explain that math problems can sometimes be tricky, but we have super tools to solve them.

Comparing with Addition: 'How Many More?'

Example:

Sarah has 5 stickers.
Tom has 3 stickers.

How many more stickers does Sarah have than Tom?

Equation: 5 - 3 = 2

Keywords: more than, less than, difference

Introduce the idea that 'comparing' can happen in different ways. Start with a simple additive comparison example.

Comparing with Multiplication: 'Times As Many'

Example:

Lily has 3 pencils.
Mark has twice as many pencils as Lily.

How many pencils does Mark have?

Equation: 3 x 2 = 6

Keywords: times as many, twice, triple

Now, introduce a multiplicative comparison example. Highlight the difference in language and what it implies.

What's the Big Difference?

Additive Comparison:

  • Tells you how much more or less one quantity is than another.
  • Uses addition (+) or subtraction (-).

Multiplicative Comparison:

  • Tells you how many times one quantity is as large as another.
  • Uses multiplication (x) or division (÷).

Summarize the key difference: addition/subtraction for 'how many more/less', and multiplication/division for 'times as many'.

Math Detective's Glossary!

Let's learn some important math words!

  • Equation: A math sentence that shows two things are equal, using an = sign. (Like 5 + 3 = 8)
  • Variable: A letter (like x or n) that stands for an unknown number in an equation. It's the mystery number!
  • Product: The answer you get when you multiply numbers. (Like 3 x 4 = 12, 12 is the product!)
  • Associative Property: When you add or multiply, you can group the numbers differently and still get the same answer! (Example: (2 + 3) + 4 = 2 + (3 + 4))
  • Commutative Property: When you add or multiply, you can change the order of the numbers and still get the same answer! (Example: 2 + 3 = 3 + 2)
  • Distributive Property: Multiplying a number by a group of numbers added together is like multiplying it by each number separately and then adding them up! (Example: 2 x (3 + 4) = (2 x 3) + (2 x 4))

Explain these key vocabulary words. Emphasize that understanding these terms helps us talk about and solve problems. Use simple examples for each property. Point out that 'variable' and 'equation' are already concepts we're using!

Two-Step Trouble Shooters

Many problems need TWO steps to solve!

Strategy:

  1. Read the problem carefully.
  2. Identify the first question.
  3. Solve the first step.
  4. Use that answer to solve the second question!

Introduce the concept of a two-step problem. Emphasize breaking it down.

Problem 1: The Lemonade Stand

Mia sold 15 cups of lemonade on Monday.
She sold 8 more cups on Tuesday than on Monday.
How many cups did she sell altogether on Monday and Tuesday?

Step 1: Cups sold on Tuesday.
Equation: 15 + 8 = T
T = 23

Step 2: Total cups sold.
Equation: 15 + 23 = C
C = 38

Mia sold 38 cups of lemonade.

Work through a two-step problem involving addition and subtraction. Model writing the equations.

Problem 2: The Toy Store

A toy store has 4 shelves of toy cars, with 12 cars on each shelf.
They sell 7 cars.
How many toy cars are left?

Step 1: Total toy cars.
Equation: 4 x 12 = C
C = 48

Step 2: Cars left.
Equation: 48 - 7 = L
L = 41

There are 41 toy cars left.

Work through a two-step problem involving multiplication and addition/subtraction. Show how to represent the unknown with a letter.

Remainders: What Do They Mean?

Sometimes, when you divide, you have some leftover!

Example: You have 10 cookies and want to give 3 cookies to each friend.

10 ÷ 3 = 3 with a remainder of 1.

What does the remainder mean here? It means 1 cookie is leftover and can't be given to a friend if you're giving out 3 to each!

Introduce the idea of remainders and how to interpret them in context.

Estimate to Check Your Work!

Is your answer reasonable?

Estimation helps you make a smart guess BEFORE you solve.

If your calculated answer is far from your estimate, you might have made a mistake!

Example: If you estimate 50, but get 5, something is wrong!

Emphasize the importance of estimation to check if answers are reasonable.

Time for Action!

Get Ready to Problem Solve!

  • Work with your group.
  • Read each problem carefully.
  • Figure out the steps.
  • Write equations with a letter for the unknown.
  • Estimate to check your answers!

Transition to the activity. Explain that students will apply what they've learned.

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Script

Teacher Script: Operation Combat

Warm-Up: What's the Difference? (10 minutes)

(Display Comparing Warm-Up slide)

"Good morning, future math warriors! Let's get our brains warmed up with a quick activity. Take a look at these two questions on the screen."

"With a partner or in your small groups, discuss how you would answer question 1 and question 2. What do you notice about how you explain the relationship in each? Think about the type of comparison you're making."

(Allow 5 minutes for discussion. Circulate and listen for keywords like 'more,' 'less,' 'times,' 'double.')

"Alright, let's hear some of your thoughts. For the first question, Sarah has 5 apples and Tom has 2. How many more stickers does Sarah have?"
(Expected student response: Sarah has 3 more apples.)

"Excellent! How did you figure that out? What operation did you use?"
(Expected student response: Subtraction, 5 - 2 = 3.)

"Now, for the second question, you have 6 cookies and your friend has 3. How would you explain that relationship?"
(Expected student response: I have twice as many cookies, or my friend has half as many.)

"Fantastic! What operation does 'twice as many' or 'half as many' make you think of?"
(Expected student response: Multiplication or division.)

"That's a great observation! Today, we're going to dive deeper into these different ways of comparing and use them to solve some exciting two-step word problems. It's like being a detective, finding clues to solve a mystery!"

(IEP/ELS Differentiation): "Remember, for our discussion, you can use sentence starters like: 'I think the difference is...' or 'One way to explain it is...'

Introduction: Unpacking Problem Combat (15 minutes)

(Display Operation Comparison Combat Slides - Slide 1: Welcome, Math Warriors!)

"Alright, brave math warriors! Today, our mission is clear: we are going to conquer two-step word problems! That means problems that need two different math steps to find the answer. We'll also learn to use estimation to check our answers, master tricky remainders when we divide, and write awesome equations with a letter standing for the unknown quantity – like a secret code to unlock the answer!"

(Display Operation Comparison Combat Slides - Slide 2: Comparing with Addition: 'How Many More?')

"Let's revisit our warm-up idea. When we compare using addition or subtraction, we're often asking 'how many more?' or 'how many less?'. Look at this example: Sarah has 5 stickers, Tom has 3 stickers. How many more stickers does Sarah have?"

"We use subtraction to find the difference. 5 - 3 = 2. Sarah has 2 more stickers. Keywords like 'more than,' 'less than,' and 'difference' are our clues for this type of comparison."

(Display Operation Comparison Combat Slides - Slide 3: Comparing with Multiplication: 'Times As Many')

"Now, for a different kind of comparison! Sometimes, one thing is 'so many times as many' as another. Like in this example: Lily has 3 pencils. Mark has twice as many pencils as Lily. How many pencils does Mark have?"

"'Twice as many' means 2 times as many. So, we multiply: 3 x 2 = 6. Mark has 6 pencils. Keywords here are 'times as many,' 'twice,' or 'triple.' These words tell us to multiply or divide."

(Display Operation Comparison Combat Slides - Slide 4: What's the Big Difference?)

"Let's put it simply: Additive comparison is about how much more or less something is – we add or subtract. Multiplicative comparison is about how many times something is bigger or smaller – we multiply or divide. Keeping these clues in mind will help us solve tough problems!"

(Display Operation Comparison Combat Slides - Slide 5: Math Detective's Glossary!)

"Before we dive into solving more problems, let's unlock some important math words that will help us communicate like true math detectives!"

"First up, Equation. An equation is a math sentence that shows two things are equal, like 5 + 3 = 8. We'll be writing lots of these!"

"Next, Variable. Remember how we've been using letters like 'T' for Tuesday's sales or 'C' for total cars? Those letters are called variables! A variable is a letter that stands for an unknown number in an equation. It's the mystery number we're trying to find!"

"And then, Product. We've been multiplying, and the answer you get when you multiply numbers is called the product. For example, in 3 x 4 = 12, the number 12 is the product!"

"Now for some special properties of numbers! First, the Associative Property. This sounds fancy, but it just means that when you are adding or multiplying numbers, you can group them differently, and the answer will still be the same. Like (2 + 3) + 4 is the same as 2 + (3 + 4)! The friends might sit in different groups, but everyone is still there!"

"Then we have the Commutative Property. This means that when you're adding or multiplying numbers, you can change the order of the numbers, and the answer stays the same! For example, 2 + 3 is the same as 3 + 2. It's like changing the order of your clothes, but you still have all the same clothes!"

"Finally, the Distributive Property. This one helps us with bigger multiplication problems! It means multiplying a number by a group of numbers added together is the same as multiplying that number by each number in the group separately, and then adding those products together. For example, 2 x (3 + 4) is the same as (2 x 3) + (2 x 4). It helps us break down big problems into smaller, easier ones!"

(IEP/ELS Differentiation): "I'm highlighting keywords on the slide. These words are important clues! We'll also review our math vocabulary: 'sum' means add, 'product' means multiply, 'quotient' means divide, and 'difference' means subtract. We just learned about 'Equation,' 'Variable,' 'Associative Property,' 'Commutative Property,' and 'Distributive Property' too!"

Guided Practice: Two-Step Takedown (20 minutes)

(Display Operation Comparison Combat Slides - Slide 6: Two-Step Trouble Shooters)

"Many problems are like puzzles with two parts! You have to solve the first part to get the information you need for the second part. Think of it like a scavenger hunt!"

"Here's our strategy: 1. Read carefully. 2. Find the first question. 3. Solve it. 4. Use that answer for the second question!"

(Display Operation Comparison Combat Slides - Slide 7: Problem 1: The Lemonade Stand)

"Let's try one together. Read this problem silently with me: 'Mia sold 15 cups of lemonade on Monday. She sold 8 more cups on Tuesday than on Monday. How many cups did she sell altogether on Monday and Tuesday?'"

"What's the first thing we need to find out?"
(Expected student response: How many cups she sold on Tuesday.)

"Exactly! If she sold 8 more cups on Tuesday than Monday, what operation will we use?"
(Expected student response: Addition.)

"Right! So, Step 1: 15 + 8. Let's use the letter 'T' for Tuesday's sales. Our equation is 15 + 8 = T. What is T?"
(Expected student response: T = 23.)

"Great! Now we know she sold 23 cups on Tuesday. What's the second question we need to answer?"
(Expected student response: How many cups altogether on Monday and Tuesday.)

"Perfect! 'Altogether' tells us to add again. So, Step 2: 15 (Monday) + 23 (Tuesday) = C (Total cups). What is C?"
(Expected student response: C = 38.)

"So, Mia sold 38 cups of lemonade. See how we used the answer from Step 1 to solve Step 2?"

(IEP/ELS Differentiation): "I've shown you the equations. You can use these to help you break down the problems. We can also use graphic organizers if you like, to put the numbers in the right places."

(Display Operation Comparison Combat Slides - Slide 8: Problem 2: The Toy Store)

"Let's tackle another one: 'A toy store has 4 shelves of toy cars, with 12 cars on each shelf. They sell 7 cars. How many toy cars are left?'"

"What's the first thing we need to figure out here?"
(Expected student response: The total number of toy cars.)

"How can we find the total number of cars if there are 4 shelves with 12 cars on each?"
(Expected student response: Multiply 4 x 12.)

"Great! Let's use 'C' for the total cars. So, Step 1: 4 x 12 = C. What does C equal?"
(Expected student response: C = 48.)

"Fantastic! Now we know there are 48 cars. What's the second step to find out how many are left?"
(Expected student response: Subtract the 7 cars they sold.)

"Exactly! So, Step 2: 48 - 7 = L (Cars Left). What is L?"
(Expected student response: L = 41.)

"There are 41 toy cars left! You are becoming problem-solving masters!"

(Display Operation Comparison Combat Slides - Slide 9: Remainders: What Do They Mean?)

"Sometimes, when we divide things, we have a little bit leftover. These are called remainders. Imagine you have 10 cookies and you want to give 3 cookies to each friend."

"If we do 10 ÷ 3, we get 3 with a remainder of 1. What does that '1' mean in this problem?"
(Expected student response: One cookie is left over, or one cookie doesn't get a friend.)

"That's right! It means you can give 3 cookies to 3 friends, and there's 1 cookie left that doesn't make a full group of 3. We have to think about what the remainder means in the context of the problem. Sometimes we ignore it, sometimes we round up, sometimes it's the answer!"

(Display Operation Comparison Combat Slides - Slide 10: Estimate to Check Your Work!)

"Before we solve a problem exactly, it's super helpful to make an estimate. An estimate is like making a smart guess, rounding numbers to make them easier to work with. If your final answer is very, very different from your estimate, it's a signal that you might need to check your work!"

"For example, if you estimated an answer around 50, but your final calculation gives you 5, something is probably wrong! Estimation is your math superpower for double-checking!"

Activity: Problem-Solving Practice (20 minutes)

(Display Operation Comparison Combat Slides - Slide 11: Time for Action!)

"Now it's your turn to be problem-solving detectives in your groups! I'm going to give each group some Problem-Solving Practice Activity cards with two-step word problems."

"Your task is to work together, read each problem carefully, figure out the two steps, write equations with a letter for the unknown, and most importantly: estimate to check your answers! I will be walking around to help and listen to your amazing problem-solving discussions."

(Circulate, provide support, and prompt students with questions like: 'What's the first step here?', 'What does this keyword tell you?', 'How can you estimate that?', 'What does the remainder mean in this problem?')

(IEP/ELS Differentiation): "Remember to work together! If you need a little extra help, it's okay to ask your partner. I've also made sure some of your problems are a bit simpler to get started. For our ELS students, let's use our word banks to help understand the problem."

Independent Practice: Worksheet Wizards (15 minutes)

"Great work, everyone! Now it's time to show off your individual problem-solving skills. I'm handing out the Two-Step Trouble Solvers Worksheet."

"On this worksheet, you'll find a few more two-step word problems. Remember our strategies: read carefully, identify the two steps, write your equations with a letter for the unknown, show your work, and don't forget to estimate to check if your answers are reasonable!"

"I'll be collecting these to see all your fantastic work. Do your best!"

(Circulate and provide individual assistance as needed.)

(IEP/ELS Differentiation): "If you need to, you can use a calculator to help you with your estimations, but try to solve the problems by hand first. If a problem has too many words, you can underline the important numbers and keywords. For IEP students, you might only need to complete a selection of the problems, or we can use our vocabulary list to help."

Game: Operation Chain Reaction (15 minutes)

"Alright, let's have some fun and practice our skills with a game! We're going to play Operation Chain Reaction Game. I'll explain the rules."

(Explain game rules: e.g., students solve a problem, and their answer becomes a number in the next problem for another team, creating a 'chain reaction' of problem-solving. Ensure problems involve two steps and different operations.)

"Ready, set, solve!"

(Facilitate the game, keeping track of scores and ensuring fair play.)

(IEP/ELS Differentiation): "For this game, you'll be in your pre-assigned teams with mixed abilities. This way, everyone can help each other out!"

Cool Down: Reflect and Connect (5 minutes)

(Display Reflect and Connect Cool Down slide/activity.)

"Wow, you've all done an amazing job tackling those two-step word problems today! Before we wrap up, let's take a moment to reflect. On your cool-down sheet, or just in your mind, think about these questions: What was one new thing you learned or one strategy that really helped you today? What's one question you still have?"

"You've worked incredibly hard and made great progress in becoming two-step problem combat experts!"

(IEP/ELS Differentiation): "You can reflect by drawing a picture, writing one word that describes what you learned, or just giving me a thumbs up or down on how much you understood today."

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Activity

Problem-Solving Practice Activity: Group Challenges

Instructions: Work with your group to solve these two-step word problems. For each problem:

  1. Read carefully to understand the story.
  2. Identify the two steps needed to solve it.
  3. Write an equation with a letter for the unknown quantity for each step.
  4. Estimate your answer first, then solve.
  5. Interpret remainders if division is involved.
  6. Show all your work!

Challenge 1: The Zoo Trip

There are 3 school buses, and each bus can carry 35 students. If 87 students sign up for the zoo trip, how many more students can still fit on the buses?












Challenge 2: Bake Sale Bonanza

Maria baked 4 dozen cookies for a bake sale. Her friend, David, baked half as many cookies as Maria. If they sold 50 cookies altogether, how many cookies do they have left?












Challenge 3: Sticker Collection

Liam had 75 stickers. He gave 15 stickers to his sister. Then, he bought 3 new packs of stickers, and each pack had 10 stickers. How many stickers does Liam have now?












Challenge 4: The Bookworm

A library has 12 shelves. Each shelf holds 24 books. On Monday, 15 books were checked out, and on Tuesday, twice that amount was checked out. How many books are still on the shelves?












Challenge 5: Pencil Power

Mrs. Davis bought a box of 100 pencils. She wants to give an equal number of pencils to her 23 students. How many pencils will each student get, and how many pencils will be left over for Mrs. Davis?

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Worksheet

Two-Step Trouble Solvers Worksheet

Instructions: Read each word problem carefully. Show your work in two steps. Write an equation with a letter for the unknown quantity for each step. Remember to estimate your answer first to check if it's reasonable, and interpret any remainders!


  1. The Animal Shelter
    An animal shelter had 25 dogs. Last week, 12 dogs were adopted. This week, they rescued 8 new dogs. How many dogs are at the shelter now?

    Estimate:

    Step 1 Equation & Solution:




    Step 2 Equation & Solution:




    Final Answer:




  1. The Pizza Party
    For a class party, Ms. Lee ordered 5 pizzas. Each pizza has 8 slices. If there are 20 students in the class and each student eats one slice, how many slices of pizza are left over?

    Estimate:

    Step 1 Equation & Solution:




    Step 2 Equation & Solution:




    Final Answer:




  1. The Garden Project
    Mr. Henderson bought 6 bags of soil for his garden. Each bag cost $7. He also bought a new shovel for $15. How much money did Mr. Henderson spend in total?

    Estimate:

    Step 1 Equation & Solution:




    Step 2 Equation & Solution:




    Final Answer:




  1. The Book Fair
    A school library is having a book fair. On Monday, they sold 45 books. On Tuesday, they sold twice as many books as on Monday. How many books did they sell altogether on Monday and Tuesday?

    Estimate:

    Step 1 Equation & Solution:




    Step 2 Equation & Solution:




    Final Answer:




  1. The Party Favors
    You have 38 small toys to put into party favor bags. If you want to put 3 toys into each bag, how many bags can you fill completely, and how many toys will be left over?
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Answer Key

Two-Step Trouble Solvers Answer Key

For Problem-Solving Practice Activity

Challenge 1: The Zoo Trip

  • Estimate: (Round 35 to 40, 87 to 90) 3 buses x 40 students = 120 students. 120 - 90 = 30. Expect around 30 students.
  • Step 1: Find total bus capacity.
    Equation: 3 x 35 = C
    C = 105
    Thought Process: The problem asks how many students can still fit, so first, we need to know the total capacity of all the buses combined. Since each of the 3 buses holds 35 students, we multiply.
  • Step 2: Find how many more students can fit.
    Equation: 105 - 87 = S
    S = 18
    Thought Process: Now that we know the total capacity (105) and how many students have signed up (87), we subtract to find the difference, which tells us how many more students can fit.
  • Final Answer: 18 more students can still fit on the buses.

Challenge 2: Bake Sale Bonanza

  • Estimate: (Round 4 dozen to 50, half to 25) Maria: 4 x 12 = 48 (approx 50). David: 48 / 2 = 24 (approx 25). Total baked: 50 + 25 = 75. Sold 50. Left: 75 - 50 = 25. Expect around 25 cookies.
  • Step 1: Find how many cookies Maria baked.
    Equation: 4 x 12 = M
    M = 48
    Thought Process: One dozen is 12, so 4 dozen is 4 times 12 to find Maria's total.
  • Step 2: Find how many cookies David baked.
    Equation: 48 / 2 = D
    D = 24
    Thought Process: David baked half as many as Maria, so we divide Maria's total by 2.
  • Step 3: Find total cookies baked.
    Equation: 48 + 24 = T
    T = 72
    Thought Process: To find the total cookies baked, we add Maria's and David's cookies.
  • Step 4: Find how many cookies are left.
    Equation: 72 - 50 = L
    L = 22
    Thought Process: We know the total baked and how many were sold, so we subtract to find the remaining cookies.
  • Final Answer: They have 22 cookies left.

Challenge 3: Sticker Collection

  • Estimate: (Round 75 to 80, 15 to 20, 10 to 10) Started with 80. Gave away 20: 80 - 20 = 60. Bought 3 packs x 10 stickers = 30 stickers. 60 + 30 = 90. Expect around 90 stickers.
  • Step 1: Find stickers after giving some away.
    Equation: 75 - 15 = S
    S = 60
    Thought Process: Liam started with 75 and gave away 15, so we subtract to find how many he had left after this first action.
  • Step 2: Find stickers from new packs.
    Equation: 3 x 10 = P
    P = 30
    Thought Process: He bought 3 packs with 10 stickers each, so we multiply to find the total from the new packs.
  • Step 3: Find total stickers Liam has now.
    Equation: 60 + 30 = N
    N = 90
    Thought Process: We add the stickers he had left (60) and the stickers he bought (30) to get his new total.
  • Final Answer: Liam has 90 stickers now.

Challenge 4: The Bookworm

  • Estimate: (Round 12 to 10, 24 to 25, 15 to 15) 10 shelves x 25 books = 250 books. Monday: 15. Tuesday: 2 x 15 = 30. Total checked out: 15 + 30 = 45. Books left: 250 - 45 = 205. Expect around 200 books.
  • Step 1: Find total books in the library.
    Equation: 12 x 24 = B
    B = 288
    Thought Process: To find the total number of books, we multiply the number of shelves by the number of books on each shelf.
  • Step 2: Find books checked out on Tuesday.
    Equation: 15 x 2 = T
    T = 30
    Thought Process: They sold twice as many on Tuesday as Monday, so we multiply Monday's sales by 2.
  • Step 3: Find total books checked out.
    Equation: 15 + 30 = C
    C = 45
    Thought Process: Add the books checked out on Monday and Tuesday to get the total checked out.
  • Step 4: Find books still on shelves.
    Equation: 288 - 45 = L
    L = 243
    Thought Process: Subtract the total books checked out from the initial total number of books to find how many are left.
  • Final Answer: 243 books are still on the shelves.

Challenge 5: Pencil Power

  • Estimate: (Round 100 to 100, 23 to 20) 100 pencils / 20 students = 5 pencils per student. Left over: 100 - (5 * 20) = 0. Expect about 5 pencils per student with a small remainder.
  • Step 1: Find how many pencils each student gets.
    Equation: 100 ÷ 23 = P
    P = 4 with a remainder of 8
    Thought Process: We divide the total pencils by the number of students to find out how many each student receives equally.
  • Step 2: Interpret the remainder.
    The remainder of 8 means there are 8 pencils left over after giving 4 pencils to each of the 23 students.
    Thought Process: The remainder in this context means the pencils that could not be distributed evenly among the students.
  • Final Answer: Each student will get 4 pencils, and there will be 8 pencils left over for Mrs. Davis.

For Two-Step Trouble Solvers Worksheet

1. The Animal Shelter

  • Estimate: 25 - 10 = 15. 15 + 10 = 25. Expect around 25 dogs.
  • Step 1 Equation & Solution: 25 - 12 = D1 (Dogs after adoption)
    D1 = 13
    Thought Process: Start with the initial number of dogs and subtract those adopted.
  • Step 2 Equation & Solution: 13 + 8 = D2 (Dogs at shelter now)
    D2 = 21
    Thought Process: Take the remaining dogs and add the newly rescued dogs.
  • Final Answer: There are 21 dogs at the shelter now.

2. The Pizza Party

  • Estimate: 5 pizzas x 8 slices = 40 slices. 40 - 20 students = 20 slices left. Expect around 20 slices left.
  • Step 1 Equation & Solution: 5 x 8 = S (Total slices)
    S = 40
    Thought Process: Multiply the number of pizzas by the slices per pizza to get the total slices.
  • Step 2 Equation & Solution: 40 - 20 = L (Slices left over)
    L = 20
    Thought Process: Subtract the number of slices eaten by students from the total slices.
  • Final Answer: There are 20 slices of pizza left over.

3. The Garden Project

  • Estimate: 6 bags x $7/bag = $42 (approx $40). $40 + $15 = $55. Expect around $55.
  • Step 1 Equation & Solution: 6 x 7 = C1 (Cost of soil)
    C1 = 42
    Thought Process: Multiply the number of bags by the cost per bag to find the total cost of the soil.
  • Step 2 Equation & Solution: 42 + 15 = C2 (Total spent)
    C2 = 57
    Thought Process: Add the cost of the soil to the cost of the shovel to find the total money spent.
  • Final Answer: Mr. Henderson spent $57 in total.

4. The Book Fair

  • Estimate: Monday: 45 (approx 40). Tuesday: 2 x 40 = 80. Total: 40 + 80 = 120. Expect around 120-130 books.
  • Step 1 Equation & Solution: 45 x 2 = T (Books sold Tuesday)
    T = 90
    Thought Process: Since Tuesday sold twice as many as Monday, multiply Monday's sales by 2.
  • Step 2 Equation & Solution: 45 + 90 = B (Total books sold)
    B = 135
    Thought Process: Add Monday's sales to Tuesday's sales to find the total number of books sold.
  • Final Answer: They sold 135 books altogether on Monday and Tuesday.

5. The Party Favors

  • Estimate: 38 toys / 3 toys/bag. 39 / 3 = 13 bags. Expect around 12-13 bags with a small remainder.
  • Step 1 Equation & Solution: 38 ÷ 3 = B (Bags filled)
    B = 12 with a remainder of 2
    Thought Process: Divide the total number of toys by the number of toys per bag to find how many bags can be filled.
  • Step 2: Interpret the remainder.
    The remainder of 2 means there are 2 toys left over that cannot make a complete bag of 3 toys.
    Thought Process: The remainder represents the toys that are not enough to fill another party favor bag.
  • Final Answer: You can fill 12 bags completely, and there will be 2 toys left over.
lenny
lenny

Game

Operation Chain Reaction Game

Goal: Teams solve two-step problems, passing their answer to the next team to use in their problem. The chain reaction continues until a final answer is reached!

Players: 2-4 teams

Materials:

  • Index cards with problems (provided below)
  • Whiteboards or scratch paper for each team
  • Markers
  • Timer (optional)

How to Play:

  1. Setup: Divide the class into teams. Give each team a whiteboard/paper.
  2. Start the Chain: Team 1 receives Problem Card A.
  3. Solve & Pass: Team 1 works together to solve Problem Card A (which is a two-step problem). Once they have their final numerical answer, they write it clearly on a smaller slip of paper and pass it to Team 2.
  4. Continue the Chain: Team 2 receives Problem Card B. Problem Card B will include a blank where Team 1's answer should go. Team 2 uses Team 1's answer to solve their two-step problem. They then pass their final numerical answer to Team 3.
  5. Final Reaction: The game continues until all problems are solved or a set time runs out. The last team to solve their problem correctly, using the previous team's answer, wins!
  6. Scoring (Optional): Points can be awarded for correct answers, showing all work, and fastest completion.

Game Problems:


Problem Card A (Start with Team 1)

Sarah bought 3 packs of stickers. Each pack had 15 stickers. She gave 5 stickers to her brother. How many stickers does Sarah have now?

Show your work and equation(s)!







Answer to pass to Team 2: __________


Problem Card B (Use Team 1's answer)

Team 1 passed you the number: [Team 1's Answer].

There were [Team 1's Answer] apples in a basket. A farmer picked 2 times as many apples on Tuesday as were in the basket. He then sold 20 apples. How many apples does the farmer have left?

Show your work and equation(s)!







Answer to pass to Team 3: __________


Problem Card C (Use Team 2's answer)

Team 2 passed you the number: [Team 2's Answer].

A baker made [Team 2's Answer] cupcakes. He put them into boxes of 6 cupcakes each. If he sold 8 boxes, how many cupcakes does he have left that are not in a full box?

Show your work and equation(s)! (Remember remainders!)







Answer to pass to Team 4: __________


Problem Card D (Use Team 3's answer)

Team 3 passed you the number: [Team 3's Answer].

There were [Team 3's Answer] pencils in a classroom. The teacher bought 2 dozen more pencils. Then, she divided all the pencils equally among 10 students. How many pencils did each student get? (You do not need to interpret the remainder for this problem).

Show your work and equation(s)!







Final Answer: __________


(IEP/ELS Differentiation): Teams will be mixed ability. Encourage students to help each other understand the problems and explain their steps. Visual aids (like drawing pictures for problems) can be used. For ELS students, key vocabulary in the problems can be pre-taught or provided with definitions.

lenny
lenny

Cool Down

Reflect and Connect Cool Down

Instructions: Take a few moments to think about today's lesson on solving two-step word problems. Answer one or more of the questions below.

  1. What was one new strategy you learned today that will help you solve two-step word problems?






  2. How is comparing with multiplication different from comparing with addition? Give an example.






  3. What is one thing you still have a question about regarding two-step word problems or remainders?






  4. Draw a picture of a two-step word problem and explain how you would solve it.












(IEP/ELS Differentiation): You can choose to answer one of the questions, draw a picture, or simply give a thumbs up/down to show how well you understand today's lesson.

lenny
lenny
Operation Comparison Combat • Lenny Learning