Problem
Ten hundreds make one thousand
Sophie has 3 ten-dollar bills and 20 dimes. Find the total amount of money she has.
Base-ten numbersMeasurement & data
Your answer
dollars
Watch out Don't just add the counts of 3 bills and 20 dimes — turn each pile into its dollar value first, because a bill and a dime are not worth the same.
How to solve
Strategy Analyze the Units — There are two kinds of money, so I find the value of each group separately by tracking its units (bills to dollars, dimes to dollars) and then add the two totals.
1STEP 1
Value of the ten-dollar bills
Each bill is worth ten dollars, and there are 3, so the bills come to $30.
3 × 30
Three tens make thirty, just like counting 10, 20, 30.
2.MD.C.8Identify Subproblems2STEP 2
Value of the dimes
Ten dimes make a dollar, so 20 dimes are 200 cents, which is $2.
20 × 10 cents = 200 cents = $2
Because ten dimes equal a dollar, 20 dimes equal 2 dollars, the same way ten hundreds make a thousand.
2.MD.C.8Analyze The UnitsThe 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 amounts
Add the two piles: 2 from the dimes makes $32.
2 = $32
The total money is just the dollar amounts of each group added together.
2.MD.C.8Identify SubproblemsAnswer
32 dollars
2 = $32
The bills alone are 30 and a small pile of dimes adds only a couple dollars, so a total near 32 is sensible; 200 cents is exactly 2, confirming $32.
Takeaway
Ten dimes bundle up into a dollar, so 20 dimes are just $2 to add to your bills!
- Value of the ten-dollar bills
- Value of the dimes
- Add the two amounts
Where next?
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