Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Browse grades and teaching videos01 · Read and understand
What you will learn
- Read thousands, hundreds, tens, and ones.
- Connect a numeral to expanded form.
- Check a total with an estimate.
Before you start
Count to 100 and multiply whole numbers by 10, 100, and 1,000.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
A school has 3 cartons holding 1,000 pencils each, 4 bundles of 100, 7 packs of 10, and 6 loose pencils. How many pencils are there?
Why this math matters
Place value lets a short numeral describe thousands of objects. Grouping works because ten ones can be exchanged for one ten without changing the total. Inventory counts, scoreboard totals, and measurements all depend on this structure.
Set up the model
A useful answer starts with clear assumptions:
- Every carton, bundle, and pack contains its stated quantity.
- The groups do not overlap, and no pencils are missing.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Count a supply room without counting every pencil
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A school has 3 cartons holding 1,000 pencils each, 4 bundles of 100, 7 packs of 10, and 6 loose pencils. How many pencils are there?
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Value each group
3 × 1,000 = 3,000; 4 × 100 = 400; 7 × 10 = 70
The group size determines each digit's contribution. Three cartons means three thousands, not three individual pencils.
Combine the contributions
3,000 + 400 + 70 + 6 = 3,476 pencils
Write one digit in each position. Reading the result aloud helps connect the symbols to the original groups.
Check and regroup
3,476 = 34 hundreds + 7 tens + 6 ones; approximately 3,500
Trading the three thousands for thirty hundreds preserves the count. Rounding to the nearest hundred gives a quick size check.
The result
The supply room contains 3,476 pencils.
A zero would still need a place in the numeral if one group size were absent. For example, no hundreds in this inventory would give 3,076, not 376.
Common mistakes to catch
- Concatenating group counts without their place values can change the total.
- An estimate such as 3,500 should not replace an exact inventory record.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Write the count for 2 thousands, no hundreds, 5 tens, and 9 ones.
Show a hint
Keep a zero in the hundreds position.
Reveal answer and explanation
2,059
2,000 + 0 + 50 + 9 = 2,059. The zero preserves the positions of the other digits.
Practice 2
How does the value of 8 change between 4,862 and 4,682?
Show a hint
Identify its position in each numeral.
Reveal answer and explanation
It changes from 800 to 80.
The first 8 is in the hundreds place; the second is in the tens place. Moving one place right divides its contribution by ten.
Take the idea with you
Explain a four-digit attendance count using bundles, then reconstruct the numeral from a different grouping.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Add a shopping total with decimal place value
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