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Explore this unit in three lessons
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How does a digit’s position help us build, compare, and estimate a number?
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Make it. Move it. Tell it.
Number Depot: build a paper shipment
I can build a big number. I can show which number is greater. I can find the nearest hundred.
Off-screen quest
Try this with a grown-up, in class, or on your own when safe. You can also use the lesson below. This quest is your choice.
Open off-screen quest + Parent Guide
Your quest
Get ready
Get paper and a pencil. No blocks are needed.
Words and source clues
Place value
A digit’s place tells what it is worth.
Expanded form
Add the value of each place.
Expanded notation
Multiply each digit by its place value. Then add.
Round
Use a nearby number. Today, find the nearest hundred.
Screen burst: 15:0015 minutes max
Your guide is getting ready.
Paper quest steps
Screen burst 1
Your depot needs a new label! Look at 31,407. Read the place names with a grown-up. Then take the quest to paper.
Offscreen: build
Write 31,407 above your chart. Put each digit in its place. Draw marks to show each group. Leave the tens place empty. Write 0 there. Tell what each group is worth. Write the parts as a sum. Then write each digit × its place value.
Offscreen: compare
Write 31,047 on a new row. Look from left to right. Stop at the first place that differs. Which number is greater? Name that place. Use < or > to show your answer.
Offscreen: round
Draw a line from 31,400 to 31,500. Mark 31,450 in the middle. Put 31,407 on the line. Which end is closer? Write “about” before your rounded number.
Screen burst 2
Show your paper work. Tell why the zero matters. Then try one Number Depot step. Use your chart if you need help. You may stop and come back to the paper quest.
Use your paper chart. Build 31,407. Compare it with 31,047. Draw the line from 31,400 to 31,500. Tell a grown-up what you found.
Grown-up note: Supported practice is not an independent assessment. This guide is not shown during mission play, independent practice, or the learning check. The timer is a reminder for this guide, not a device-wide limit. It stops new guide steps, not the rest of the lesson, and never saves, submits, or grades work. Only an anonymous timer deadline is kept in this tab’s session storage; no answers, notes, or account IDs. If storage is blocked, the reminder lasts only in this open page. A grown-up can use a separate timer too. After a real off-screen break, choose a new burst when ready.
Look closely. Make a connection.
Build a number, then defend its size
Your learning mission / Tu misión de aprendizaje
Build a number, then defend its size
✦
01
LO · Learning Objective / Objetivo
By the end, I can…
Represent numbers through 100,000 using place-value parts.
Compare whole numbers by the first different place.
Use neighboring hundreds to round and explain an estimate.
02
Essential Question / Pregunta esencial
How does a digit’s position help us build, compare, and estimate a number?
03
Success Criteria / Criterios de éxito
Correct expansion with the empty tens place preserved
Correct comparison symbol
Reasoning names the first differing place
Skills & Standards / Habilidades y estándares
3.2A · Compose and decompose whole numbers through 100,000, including expanded notation. · 3.2B · Explore ten-to-one exchanges, including ten 10,000 cards for 100,000 in the linked lesson. · 3.2C · This unit practices nearest-hundred rounding on number lines; other intervals in 3.2C are not taught here. · 3.2D · Compare and order whole numbers through 100,000 using comparison symbols.
04
DOL · Demonstration of Learning / Demostración
Use place value, rather than the number of visible nonzero digits, to restore the depot.
Build the label 32,406. Use standard place-value digits: no more than 9 pieces of each kind.
Arrange shipment counts from least to greatest.
A label reads 18,275. Which estimate to the nearest hundred belongs on its cart?
Compare 31,407 with 31,047. Write an expanded form and identify the first place that proves your comparison.
Separate learning check: 4 of 5 correct (80% target).
Our base-ten system groups ten ones into one ten, ten tens into one hundred, and ten hundreds into one thousand. A zero keeps an empty place visible. In 24,306, the 3 represents 300, not 3. Expanded form adds its place values: 20,000 + 4,000 + 300 + 0 + 6. Expanded notation shows each digit times its place value: (2 × 10,000) + (4 × 1,000) + (3 × 100) + (0 × 10) + (6 × 1). Both equal 24,306. Zero terms may be left out of either sum, but the numeral still needs its zero.
The Number Depot build uses five places, from ones through ten thousands, with at most nine pieces per place. Its largest possible label is 99,999. In the linked Build and exchange place-value parts lesson, ten 10,000 cards trade for one 100,000 card. That exchange uses a sixth place; it is not another piece to find in this mission.
To compare, start at the largest place and move right until the digits differ. For rounding to hundreds, find the hundred below and above the number. The midpoint is 50 after the lower hundred. Choose the closer endpoint; at the midpoint, choose the higher one.
Watch the thinking
Which delivery is larger: 24,306 or 24,360?
1
Both numbers have 2 ten thousands, 4 thousands, and 3 hundreds.
2
Compare tens: 0 tens is less than 6 tens. Therefore 24,306 < 24,360.
3
24,306 is between 24,300 and 24,400. It is 6 from 24,300 and 94 from 24,400.
24,360 is larger. Rounded to the nearest hundred, 24,306 is 24,300.
Words that help
Place value
Place value depends on position. In this model, the left column represents tens and the right column ones: one bead in the tens column represents ten, while one bead in the ones column represents one. Likewise, the digit 1 has different values in 10 and 1. View full-size image / Ver imagen completaThe value a digit has because of its position.
Add digit × place-value terms. Expanded form adds the resulting place values; both name the same number.
Round
Rounding names a nearby multiple of a chosen place value. If the path runs from 0 at the left endpoint to 10 at the right, the marker at 8 is nearer 10, so 8 rounds to 10 to the nearest ten. View full-size image / Ver imagen completaName a nearby multiple of a chosen place value.
Standards connections and official sources
These focused activities address the listed expectations. Completing a unit is practice evidence, not certification of mastery or full-year standards coverage.
Compare and order whole numbers through 100,000 using comparison symbols.
Grade 3 · Number Depot: place-value sample · Public sample
Try a sample quiz or sample test
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Number Sense & Place Value · Grade 3 | MasteryTrail
