Problem
Ten hundreds make one thousand
Sophie has 3 thousand-dollar checks and 20 hundred-dollar bills. How much money does she have in all?
Base-ten numbersMeasurement & data
Your answer
dollars
Watch out Don't read the 20 bills as just 20 — ten hundred-dollar bills bundle into one thousand-dollar unit.
How to solve
1STEP 1
Value of the thousand-dollar checks
3 thousand-dollar checks are three thousands — $3000.
3 × 1000 = 3000
Three thousands make three thousand, just like counting one thousand, two thousand, three thousand.
Identify Subproblems2.MD.C.82STEP 2
Value of the hundred-dollar bills
10 hundred-dollar bills bundle into one thousand, so 20 of them are two bundles — $2000.
100 × 10 = 1000 → 100 × 20 = 2000
Each bill is the same value, so 20 of them are 20 equal groups; and since ten of them gather into one larger unit, 20 bills hold two of those bundles, worth two thousand dollars.
Analyze UnitsPlace Value Chart2.MD.C.84.NBT.A.2The 20 dimes are worth $2 in all.
Why?
Each dime is the same 10 cents, so 20 dimes are 20 equal groups of ten cents, which comes to 200 cents.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Changing 200 cents into dollars means bundling every 100 cents into one dollar, and 200 cents holds two of those hundreds, so it is $2.
Why?
Ten cents make one ten and ten of those tens make one hundred, so 100 cents gathers into a single dollar.
🧱Place-value groupingTen ones make one ten and ten tens make one hundred — each place bundles ten of the last.
3STEP 3
Add the two values
Add the $3000 and the $2000 to get $5000!
3000 + 2000 = 5000
The total is just the value of each group added together, so one kind's value plus the other's is all the money.
Identify Subproblems2.MD.C.8Answer
5000 dollars
3000 + 2000 = 5000
Check — count everything in hundred-dollar units: the 3 thousand-dollar checks are 30 hundreds, plus the 20 hundred-dollar bills, is 50 hundreds in all = $5000.
Takeaway
Don't count piece by piece — bundle by units. Ten hundred-dollar bills make one thousand-dollar bundle, so 20 of them are quickly $2000.
- 3 checks → $3000
- 20 bills → $2000 (ten hundreds bundle up)
- Add up → $5000
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