Mixed Operations and Real-World Problem Solving

Free sample questions, a clear explanation, and 5 practice skills with an AI tutor that guides without giving the answer away.

Math Detectives: Solving Real-World Puzzles!

Hello, Super Solver! Did you know that math isn't just about numbers on a page? It's a secret code for solving puzzles in the real world! Imagine we are planning a big fundraiser to buy a new plant for our classroom. We'll sell yummy cookies and cool pencils. Using our math skills is like being a detective—we use clues to find the answer!

Let's start with a simple clue. If you sell 8 chocolate chip cookies and then 6 oatmeal cookies, how many did you sell in all? We can draw a bar model to see the parts. The 8 cookies are one part, and the 6 cookies are the other part. When we put them together, we find the whole!
8 + 6 = 14 cookies sold. Awesome!

What if we start with 15 pencils and sell 7? To find out how many are left, we use subtraction. Our bar model shows the whole (15) and the part we sold (7). The mystery is finding the part that is left!
15 - 7 = 8 pencils left. You solved it!

Your Super Solver Toolkit!

Bar Models: Help us SEE the story problem by showing the 'parts' and the 'whole'.
Number Bonds: Show how numbers are connected and can be broken apart or put together.
Number Sentences: The secret code we write to find the final answer (like 8 + 6 = 14).

Sometimes, there are two steps in a puzzle! Let's say you have 18 stickers. You sell 5 in the morning and 4 in the afternoon. How many are left?
Step 1: First, let's find out how many you sold altogether. 5 + 4 = 9 stickers.
Step 2: Now, we take away the total sold from the start. 18 - 9 = 9 stickers left.
See? You just solved a two-step mystery!

Our fundraiser was a huge success! We sold 4 boxes of crayons, and each box had 10 crayons. We can count by tens to find the total: 10, 20, 30, 40. That's 4 tens, which is 40 crayons! When we plan a fundraiser, we use addition to count all the money we earn and subtraction to figure out how much is left after we pay for our supplies.

You are a fantastic problem solver! Keep using your math detective skills to find and solve puzzles everywhere you go.

Sample questions

1. Lily has 7 red apples. Her friend gives her 5 green apples. How many apples does Lily have in all?

○ 7

○ 2

✓ 12

○ 13

Answer: 12 — Count all the apples together.

2. Tom saw 8 birds on a tree. 6 more birds flew to the tree. How many birds are on the tree now?

○ 8

○ 2

○ 13

✓ 14

Answer: 14 — Add the birds that were there to the birds that flew in.

3. There are 9 blue cars and 4 yellow cars in the parking lot. How many cars are there altogether?

✓ 13

○ 5

○ 9

○ 14

Answer: 13 — Find the total number of cars.

Skills in this topic

Solve one-step addition word problems within 20 using bar models.
Solve one-step subtraction word problems within 20 using bar models.
Solve two-step word problems involving addition and subtraction within 20 using number bonds and bar models.
Apply knowledge of place value to solve problems involving numbers up to 100 (e.g., finding the total number of items in multiple groups of ten).
Design a simple plan for a class fundraiser, explaining how to use addition and subtraction to track money earned and spent.

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