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Decimals: Shading the Space Between Whole Numbers

Students shade a hundred-square grid to see that decimals are just fractions of a whole — tenths are full columns, hundredths are single squares.

Grade 4Decimals45 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
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Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Explain that decimals show parts of a whole.
  • ✓Read and write tenths and hundredths as decimals.
  • ✓Connect a decimal to its fraction (0.25 = 25/100).
  • ✓Model decimals on a hundred-square grid.
Essential Question

Money already uses decimals — $0.25 is a quarter of a dollar. So what does the number after the dot actually stand for?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Model · Interactive Tool

The Decimal Grid

Project this and shade squares. Each full column is a tenth; each square is a hundredth. Watch the decimal and the fraction update together.

🟦 Shade the grid — build a decimalTry it
Squares shaded (of 100)25

The Lesson · Gradual Release (I Do · We Do · You Do)

45 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — The Money Clue

5 min

$0.25 is part of a dollar — what part?

👩‍🏫 Teacher Moves

  • Show $0.25 and a dollar.
  • Ask what the .25 means.
  • Set the goal: decimals = parts of a whole.

🎒 Student Actions

  • Connect $0.25 to a quarter.
  • Guess what the digits after the dot mean.
  • Predict how to write “half.”
2

I Do — Shade a Tenth

10 min

Teacher models on the grid.

👩‍🏫 Teacher Moves

  • Shade one full column = 0.1 = 10/100.
  • Shade single squares = hundredths.
  • Write 0.25 and 25/100 together.

🎒 Student Actions

  • Copy the shaded grid.
  • Name a tenth and a hundredth.
  • Write the decimal and fraction.
3

We Do — Shade Together

12 min

Class drives the Decimal Grid.

👩‍🏫 Teacher Moves

  • Build tenths, then hundredths.
  • Read each as a decimal and a fraction.
  • Compare 0.3 and 0.30.

🎒 Student Actions

  • Shade to hit a target decimal.
  • Read decimal + fraction.
  • Notice 0.3 = 0.30.
4

You Do — On Your Own

13 min

Students read and write decimals.

👩‍🏫 Teacher Moves

  • Assign decimals to shade and write.
  • Include matching decimal to fraction.
  • Add comparing two decimals.

🎒 Student Actions

  • Shade and label decimals.
  • Match decimals to fractions.
  • Compare two decimals.
5

Close — Read the Dot

5 min

Write one decimal together.

👩‍🏫 Teacher Moves

  • Name an amount; students write it.
  • Confirm tenths vs. hundredths.
  • Hand out the exit ticket.

🎒 Student Actions

  • Write the decimal for an amount.
  • Explain the place after the dot.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics, including the Standards for Mathematical Practice.

CCSS
4.NF.C.6

Use decimal notation for fractions with denominators 10 or 100.

CCSS
4.NF.C.5

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and add them.

CCSS
5.NBT.A.3

Read, write, and compare decimals to thousandths.

SMP
MP.7

Look for and make use of structure in the base-ten (and decimal) system.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Use money as a familiar decimal anchor.
  • Sentence frame: “___ hundredths equals 0.___.”
  • Shade grids by hand before the on-screen tool.

Support & Access

IEP / 504
  • Start with tenths (full columns) only.
  • Provide pre-printed hundred grids.
  • Link every decimal to a money amount.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Extend to thousandths.
  • Place decimals on a number line.
  • Add two decimals using the grid.
Materials

What to gather

  • 📽️Projector / board
  • 📓Math notebooks
  • 💻The Decimal Grid
  • 💵Play money
  • 📐Hundred-square grids
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

decimala number showing parts of a wholedecimal pointthe dot separating whole from partstenthone of ten equal parts (0.1)hundredthone of a hundred equal parts (0.01)wholethe complete amount (1.0)place valuethe value a digit has by its placefractiona number of equal partsequivalentequal in value
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
Write 7 tenths as a decimal and a fraction.
0.7 = 7/10 (or 70/100).
QUESTION 2
What does the 3 in 0.35 stand for?
3 tenths (0.30) — it is in the tenths place, so it means 30 out of 100.
QUESTION 3
Which is greater, 0.4 or 0.40? Explain.
They are equal — 0.4 means 4 tenths and 0.40 means 40 hundredths, which are the same amount.

Going deeper? Shade a decimal design.

Have students color a hundred-grid to make a picture, then write the decimal and fraction for each color used. A printable hundred-grid is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Decimals: Tenths & HundredthsFlip
Card 1
Term
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Meaning
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Decimals: Tenths & HundredthsQuiz
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Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Decimals: Tenths & HundredthsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: decimal, decimal point, equivalent, fraction, hundredth, place value, tenth, whole
  1. the complete amount (1.0)
  2. a number showing parts of a whole
  3. one of ten equal parts (0.1)
  4. equal in value
  5. a number of equal parts
  6. the dot separating whole from parts
  7. one of a hundred equal parts (0.01)
  8. the value a digit has by its place

Part B · Show what you learned

  1. Write 7 tenths as a decimal and a fraction.
  2. What does the 3 in 0.35 stand for?
  3. Which is greater, 0.4 or 0.40? Explain.
Answer key — Part A: 1) whole · 2) decimal · 3) tenth · 4) equivalent · 5) fraction · 6) decimal point · 7) hundredth · 8) place value
Part B: 1) 0.7 = 7/10 (or 70/100). 2) 3 tenths (0.30) — it is in the tenths place, so it means 30 out of 100. 3) They are equal — 0.4 means 4 tenths and 0.40 means 40 hundredths, which are the same amount.