You're sitting at the kitchen table. They look at you. But your third grader slides a worksheet across the surface — Home Link 3-9 at the top, a grid of shaded squares, a number line, and a blank space waiting for a decimal. "What does this even mean?
It sounds simple, but the gap is usually here.
You want to help. But the way they teach fractions and decimals now? It's not how you learned it.
Here's the thing: Home Link 3-9 (from Everyday Mathematics, Grade 3) isn't just busywork. It's a carefully designed bridge between concrete models — shaded grids, number lines, fraction circles — and the abstract symbols kids will use for years. Fractions. Decimals. The connection between them.
Most adults never got this bridge. " "Flip and multiply.Here's the thing — we memorized rules. Practically speaking, "Move the decimal point. " But we didn't see it.
Your kid is getting the visual foundation. And if you understand what the lesson is actually after, you can support them without doing the work for them Took long enough..
What Is Home Link 3-9
Everyday Mathematics organizes content into units and lessons. In real terms, unit 3 in third grade focuses on fractions and decimals — specifically, representing them in multiple ways. Lesson 9 (hence 3-9) is the practice page that comes home.
The worksheet typically includes:
- A 10×10 grid (hundredths grid) with some squares shaded
- A number line marked in tenths or hundredths
- Fraction circles or strips
- Blank spaces to write the fraction and the decimal for each model
The goal? Help kids see that three-tenths, 3/10, and 0.3 are the same quantity — just written differently.
That's it. That's the whole lesson. But the implications run deep.
Why the hundredths grid matters
The 10×10 grid isn't arbitrary. It's a physical model of our base-10 system. One whole = 100 tiny squares. Each row = 10 squares = one tenth. Each square = one hundredth.
When a kid shades 3 full rows, they're not just coloring. Still, they're building 30/100. And they can see that 30/100 = 3/10 = 0.3 = 0.30.
That visual equivalence? It's the foundation for everything decimal-related that comes later — rounding, comparing, adding, subtracting, multiplying.
Why the number line matters
Grids show area. Number lines show distance and order.
A number line marked in tenths (0, 0.1, 0.2 ... 1.Day to day, 0) lets kids place 0. 3 and 3/10 at the exact same spot. Because of that, it also sets up comparison: 0. 4 is to the right of 0.3, so it's greater. No rules to memorize — just position.
Later, when they encounter 0.35, they'll know it lives between 0.3 and 0.4. Because they've seen it Simple, but easy to overlook..
Why This Lesson Matters (More Than You Think)
Third grade is the pivot point. On the flip side, before this, fractions are "parts of a whole" — pizza slices, candy bars. Decimals barely exist. After this, the two systems start talking to each other. And they keep talking through algebra, chemistry, finance, coding — you name it Easy to understand, harder to ignore..
Kids who don't build this connection early tend to hit a wall in fifth or sixth grade. Even so, 25 + 1/4, and it feels like magic. Suddenly they're asked to convert 3/8 to a decimal, or add 0.Because no one ever showed them the structure underneath.
Home Link 3-9 is that structure.
The hidden trap: "Just add a zero"
You've heard it. 3 becomes 0."To change tenths to hundredths, just add a zero — 0.Maybe you've said it. 30.
It works. They think 0.But if that's all a kid knows, they don't understand why. But 30 are different numbers that happen to be equal by a rule. Still, 3 and 0. They don't see that the grid didn't change — we just counted the same shaded area in smaller pieces.
That misunderstanding shows up later as:
- Thinking 0.4 and 0.3 (because 30 > 3)
- Struggling to compare 0.38
- Writing 0.30 > 0.5 as 0.
The grid prevents all of it. If the kid actually looks at it.
How the Lesson Works (Step by Step)
Let's walk through what a typical Home Link 3-9 asks — and how to talk through each part without taking the pencil.
1. Shaded hundredths grid → fraction and decimal
The task: A grid with 4 rows fully shaded (40 squares). Write the fraction and decimal.
What's happening: The kid counts 40 out of 100 squares. Fraction: 40/100. Decimal: 0.40 or 0.4.
Your move: Ask, "How many rows are shaded?" Not "How many squares?" Rows connect to tenths. Squares connect to hundredths. Both are valid — but rows are faster Not complicated — just consistent..
If they say "40 squares," follow up: "So that's 40 out of 100. How many rows?Can you write that as a fraction?" Four. In practice, "So it's also four-tenths. Think about it: "Now, each row is one tenth. " Good. How do we write four-tenths as a decimal?
Let them say 0.Practically speaking, 4. Then ask: "Could we also write 0.40? Why?
Basically the moment. *Ask.Don't explain. * Let them notice the extra zero doesn't change the value The details matter here. Worth knowing..
2. Number line → locate and label
The task: A number line from 0 to 1, marked in tenths. "Mark 0.3 and 3/10. Mark 0.75 and 75/100."
What's happening: Kids place a dot at the third tick mark for 0.3/3/10. For 0.75, they have to estimate between 0.7 and 0.8 — or notice the hundredth marks if the line has them.
Your move: "Where does three-tenths live?" They point. "Where does seventy-five hundredths live?" They estimate. "How do you know it's not at 0.7?" Because 75 is more than 70. "How much more?" Five hundredths Simple as that..
If the line only shows tenths, this is hard. So naturally, let them wrestle. That's intentional. It forces them to think in hundredths while looking at tenths. Don't rush to draw the hundredth marks. The struggle is the learning Less friction, more output..
3. Fraction circles / strips → multiple representations
The task: A circle divided into 10 equal parts, 6 shaded. Write the fraction and decimal.
What's happening: 6/10 = 0.6. But some kids write 0.06 (confusing tenths/hundredths place) or 6.0 (confusing part/whole) Nothing fancy..
Your move: "How many pieces total?" Ten. "How many shaded?" Six. "So what fraction?" 6/10. "How do we say that?" Six-tenths. "
Your move: "How many pieces total?" Ten. "How many shaded?" Six. "So what fraction?" 6/10. "How do we say that?" Six-tenths. "How do we write that as a decimal?" 0.6 And that's really what it comes down to..
Now ask: "If we wanted to write this using hundredths instead of tenths, what would we need?" Let them think. "Each tenth is worth how many hundredths?" Ten. "So six-tenths is how many hundredths?In practice, " Sixty. "So we could also write this as 60/100 or 0.60 Worth keeping that in mind..
We're talking about where the magic happens. Day to day, 6 and 0. They realize 0.60 are the same amount — just counted differently Most people skip this — try not to..
4. Word problems → connect to representations
The task: "Sarah ate 0.4 of a pizza. Tom ate 3/5 of a pizza. Who ate more?"
What's happening: Kid needs to compare 0.4 and 3/5. Common mistake: 0.4 > 3/5 because 4 > 3 It's one of those things that adds up. No workaround needed..
Your move: "Let's make them the same kind of number. Would you rather work with fractions or decimals?"
If they choose decimals: "3/5 as tenths? So 3 times 2 equals 6. That's why 3/5 = 6/10 = 0. /10. 2. What number times 5 equals 10? 3/5 = ?6.
Now compare: 0.4 vs 0.6. "Who ate more?" Tom.
If they choose fractions: "0.Consider this: need common denominator. In practice, 4 as tenths? Now 4/10 vs 3/5. 0.4 = 4/10. 3/5 = 6/10 The details matter here..
Same result, different path. Let them choose.
5. Equal values → multiple ways to write
The task: "Write three different ways to show 0.5."
What's happening: Some kids write 0.5, 0.50, 5/10, 50/100. Others write 0.5, 1/2, 5/10 And that's really what it comes down to. Nothing fancy..
Your move: "Can you show me 0.5 using the hundredths grid?" They shade 50 squares or 5 rows. "Can you show me 50/100?" Same shading. "Are these the same amount?" Yes Turns out it matters..
"Now can you show me 1/2?" They might shade 5 rows (tenths) or 50 squares (hundredths). In practice, "Is 1/2 the same as 0. 5?" Yes But it adds up..
This is the payoff moment. The kid discovers that different symbols can represent the exact same amount.
Why This Approach Works
You're not teaching procedures. You're teaching relationships.
If you're ask "How many rows?When you let them discover that 0.Which means " instead of "How many squares? ", you're guiding attention to the structure. So 4 = 0. 40, you're building number sense rather than memorization That's the part that actually makes a difference. Simple as that..
The grid isn't a crutch — it's a thinking tool. And the questions aren't tricks; they're invitations to notice patterns.
Common Pitfalls to Avoid
- Don't rush to algorithms. If they're counting squares on a hundredths grid, let them. They'll see the pattern eventually.
- Don't correct immediately. If they write 0.30 > 0.3, ask "Are these the same amount? How do you know?"
- Don't assume understanding. If they can label 0.4 on a number line, ask them to explain how they knew where to put it.
The Real Goal
By the end of these lessons, students should be able to:
- Explain why 0.4 = 0.40 = 4/10 = 40/100
- Choose the most efficient representation for a given problem
- Translate flexibly between fractions and decimals
- Understand that decimal places represent powers of ten, not just "digits to write"
This isn't about getting the right answer. It's about understanding the relationships between different ways of expressing the same quantity But it adds up..
The grid, the number line, the fraction circles — they're all bridges. And your questions are the scaffolding that helps students build their own understanding, one deliberate observation at a time.
