You're sitting at the kitchen table. And they look at you. 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?
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. Here's the thing — fractions. Decimals. It's a carefully designed bridge between concrete models — shaded grids, number lines, fraction circles — and the abstract symbols kids will use for years. The connection between them It's one of those things that adds up. Nothing fancy..
Most adults never got this bridge. We memorized rules. Which means "Move the decimal point. " "Flip and multiply." 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 Small thing, real impact..
What Is Home Link 3-9
Everyday Mathematics organizes content into units and lessons. Day to day, 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 Which is the point..
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? Which means 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. Worth adding: one whole = 100 tiny squares. And each row = 10 squares = one tenth. Each square = one hundredth.
When a kid shades 3 full rows, they're not just coloring. They're building 30/100. And they can see that 30/100 = 3/10 = 0.Practically speaking, 3 = 0. 30 Not complicated — just consistent..
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.Plus, 1, 0. On the flip side, 2 ... 1.But 0) lets kids place 0. 3 and 3/10 at the exact same spot. It also sets up comparison: 0.4 is to the right of 0.Practically speaking, 3, so it's greater. No rules to memorize — just position.
Later, when they encounter 0.4. 35, they'll know it lives between 0.In practice, 3 and 0. Because they've seen it Not complicated — just consistent..
Why This Lesson Matters (More Than You Think)
Third grade is the pivot point. After this, the two systems start talking to each other. Before this, fractions are "parts of a whole" — pizza slices, candy bars. Decimals barely exist. And they keep talking through algebra, chemistry, finance, coding — you name it Worth knowing..
Kids who don't build this connection early tend to hit a wall in fifth or sixth grade. In practice, suddenly they're asked to convert 3/8 to a decimal, or add 0. Plus, 25 + 1/4, and it feels like magic. Because no one ever showed them the structure underneath.
Easier said than done, but still worth knowing.
Home Link 3-9 is that structure.
The hidden trap: "Just add a zero"
You've heard it. Maybe you've said it. Still, "To change tenths to hundredths, just add a zero — 0. Think about it: 3 becomes 0. 30.
It works. But if that's all a kid knows, they don't understand why. They think 0.3 and 0.30 are different numbers that happen to be equal by a rule. They don't see that the grid didn't change — we just counted the same shaded area in smaller pieces That's the whole idea..
That misunderstanding shows up later as:
- Thinking 0.Plus, 4 and 0. Here's the thing — 30 > 0. 38
- Writing 0.Think about it: 3 (because 30 > 3)
- Struggling to compare 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 That alone is useful..
If they say "40 squares," follow up: "So that's 40 out of 100. Also, can you write that as a fraction? On the flip side, " Good. "Now, each row is one tenth. Think about it: how many rows? " Four. "So it's also four-tenths. How do we write four-tenths as a decimal?
Let them say 0.Then ask: "Could we also write 0.In real terms, 4. 40? Why?
This is the moment. Don't explain. Ask. Let them notice the extra zero doesn't change the value.
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 Surprisingly effective..
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, but easy to overlook..
If the line only shows tenths, this is hard. Now, that's intentional. It forces them to think in hundredths while looking at tenths. In practice, don't rush to draw the hundredth marks. Let them wrestle. The struggle is the learning Not complicated — just consistent..
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) Small thing, real impact..
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.
Now ask: "If we wanted to write this using hundredths instead of tenths, what would we need?"So six-tenths is how many hundredths?" Let them think. " Ten. Now, " Sixty. "So we could also write this as 60/100 or 0."Each tenth is worth how many hundredths?60.
This is where the magic happens. 6 and 0.They realize 0.60 are the same amount — just counted differently.
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 Surprisingly effective..
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? 3/5 = ?/10. Here's the thing — what number times 5 equals 10? 2. So 3 times 2 equals 6. 3/5 = 6/10 = 0.6 Simple, but easy to overlook..
Now compare: 0.4 vs 0.6. "Who ate more?" Tom Worth keeping that in mind..
If they choose fractions: "0.4 as tenths? 0.4 = 4/10. Now 4/10 vs 3/5. Need common denominator. 3/5 = 6/10.
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.
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.
"Now can you show me 1/2?5?" They might shade 5 rows (tenths) or 50 squares (hundredths). "Is 1/2 the same as 0." Yes.
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.
When you ask "How many rows?That said, ", you're guiding attention to the structure. In practice, " instead of "How many squares? When you let them discover that 0.Day to day, 4 = 0. 40, you're building number sense rather than memorization.
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.
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.
