Addition
4A · Chapter 2 · Lesson 1 · MATH-4A-C02-L01
Learning goal. Solve multi-place-value sums efficiently and explain regrouping with exchanged units.
Before you begin
Recall: 4A Ch1: million-range place value; Grade 3: column algorithms and comparison bars. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
A teacher partitions 390,500 counters into equal groups of 100. How many counters are in each group?
Show answer & reasoning
Each group has 390,500 ÷ 100 = 3,905 counters.
Calculate 23,705 + 2,031 and check by subtraction.
Show answer & reasoning
23,705 + 2,031 = 25,736; subtract 2,031 to recover 23,705.
Calculate 19,965 × 10 using place value.
Show answer & reasoning
Every place-value unit becomes 10 times as large; 19,965 × 10 = 199,650.
Key vocabulary
- regroup
- exchange equal-value units
- compensation
- temporary adjustment corrected afterward
- sum
- result of addition
- difference
- result of subtraction
Understand the concept
Large-number addition is built from equal place values. Add ones to ones, tens to tens and so on. If a column makes 10 or more units, exchange ten for one in the column to the left. Before calculating, estimate the answer to check whether carrying has been recorded in the correct place.
Model it: column alignment and ten-to-one exchange. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
Calculate 246,598 + 170,753.
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Check your understanding 1
Calculate 443,360 + 30,765.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Worked example 2
Calculate 669,167 + 164,434.
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Check your understanding 2
Calculate 650,011 + 141,884.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Worked example 3
Calculate 58,727 + 136,751.
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Check your understanding 3
Calculate 358,947 + 91,839.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Guided practice
Calculate 460,327 + 209,720.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Calculate 119,559 + 207,178.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Calculate 658,056 + 217,578.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Calculate 273,844 + 184,639.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Calculate 609,362 + 6,917.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Independent practice
Calculate 382,014 + 102,336.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Calculate 430,543 + 158,222.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Calculate 20,306 + 54,416.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Calculate 315,296 + 82,569.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Calculate 264,874 + 146,791.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Calculate 187,581 + 60,502.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Calculate 306,172 + 76,087.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Calculate 345,751 + 90,048.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
Find 43,200 + 380 without losing the hundreds and tens. Explain how place values align.
Show answer & reasoning
Add matching place-value units: 43,200+380=43,580.
Calculate 203,308 + 210,974.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Exit check
Calculate 132,512 + 197,451.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Calculate 386,455 + 28,055.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.
Calculate 125,687 + 43,497.
Show answer & reasoning
Align the place values; add ones, tens, hundreds and higher units, exchanging 10 of one unit for 1 of the next when needed.