Super Scalers Part 2: Dividing to Find “How Much for Just One?”

Hello Maths Problem Solvers! You’ve learned how to “scale up” using multiplication to find out how much you need for many items. Now, we’re going to become “Super Scalers” in reverse! We’ll learn how to scale down using division to find out how much (or how long) it takes for just one item when you know the total for a group. It’s like finding the secret value of a single piece!

What Are “Scaling Down” Problems?

“Scaling Down” problems are maths stories where you are given a total amount (like total time, total cost, or total items) for a certain number of identical things. Your mission is to use division to figure out the amount for only ONE of those things. This is also sometimes called finding the “unit rate” – the rate or cost for a single unit.

The Big Idea: If you know the total for MANY items, you can divide by the number of items to find out the value for ONE item. This is like sharing equally!

Example 1: Time per Model! Problem: “It takes 20 minutes to make 4 identical models. How long does it take to make 1 model?”

• Understand the Information: We know the total time (20 minutes) for 4 models.
• Identify the Goal: We want to find the time for 1 model.
• Choose the Operation: Since we are “scaling down” from 4 models to 1 model, or sharing the total time equally among the models, this is a job for division!
• Calculate: We need to divide the total time by the number of models.
  • So, 20 (minutes) ÷ 4 (models) = ?
  • Think: What number times 4 equals 20? (Use your 4 times table facts!)
  • 20 ÷ 4 = 5 minutes.
• Sense Check & State: It would take 5 minutes to make 1 model. (Does that make sense? If 1 model is 5 mins, then 4 models would be 5+5+5+5 = 20 mins. Yes!)

Example 2: Cost per Toy! Problem: “A pack of 3 identical toy cars costs £12. How much does one toy car cost?”

• Understand the Information: We know the total cost (£12) for 3 cars.
• Identify the Goal: We want to find the cost for 1 car.
• Choose the Operation: We’re sharing the total cost among the 3 cars to find the cost of one, so it’s division.
• Calculate: Divide the total cost by the number of cars.
  • So, £12 ÷ 3 (cars) = ?
  • Think: What number times 3 equals 12? (Use your 3 times table facts!)
  • 12 ÷ 3 = £4.
• Sense Check & State: One toy car costs £4.

Become a “Value of One” Detective! (18 Problems to Solve)

Ready to practice finding out “how much for just one?” For each problem below, read the story carefully, identify the total amount and the number of items, and then divide to find the value for a single item!

(Your web app with the 18 questions will go here. The problems should be one-step scaling down scenarios using division with whole numbers, using facts related to 3s, 4s, 8s, etc.)

Why is Understanding “Scaling Down” So Important?

• Real-Life Money Smarts: It helps you figure out the cost of a single item to see if it’s a good deal (unit price!).
• Fair Sharing: You use it whenever you need to share something equally among a group.
• Understanding Rates: It’s the first step to understanding things like speed (miles per hour) or price per item.
• Boosts Division Skills: You see a very practical use for your division facts!

Tips for Grown-Ups: Helping Your “Value of One” Finder

“Scaling down” problems, or finding the unit rate, are a fundamental application of division. They often involve partitive division (sharing).

• Identify “Total” and “Number of Items”: Help the child find these two key pieces of information in the word problem. “What’s the total amount we know? And how many items does that total belong to?”
• Visualise with Sharing: Use real objects or drawings. “Here are 20 counters representing minutes. Let’s share them out among 4 ‘model’ piles. How many in each pile?”
• Link to “Groups Of” in Reverse: If 4 groups of something make 20, then 20 divided into 4 groups will tell us what that something is.
• Emphasise the Question “How much/many for ONE?”: This helps them focus on the goal of the problem.
• Connect to Multiplication Facts: Always encourage them to use their times table knowledge by asking, “What number multiplied by [number of items] gives you [the total amount]?”