Practice · One number, many addition expressions · Sensim Math

Variant 1 easy

Decompose the number into a sum of two equal numbers and fill in the blanks.

Reading from top to bottom, the table repeatedly splits one number into a sum of two equal numbers.

Row 1: the whole bar holds $2{,}000$ .
Row 2: the $2{,}000$ from Row 1 is split into two equal numbers shown in two cells, and the right cell reads $1{,}000$ .

Fill in the blanks so that the numbers in every row add up to $2{,}000$ .

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A table splits 2000 by halving repeatedly down 2 rows. Fill the blank cells so every row still sums to 2000.

Givens

Row 1 holds 2,000 in a single full-width cell.
Each later row splits every cell above into two equal halves.
The table has 2 rows in total.

Unknowns

The blank cells in every split row.

Constraints

Each row must add up to 2000.
Within a row the cells are equal (each split is into two equal parts).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #1 Draw a Diagram

Each row repeats the same rule -- take a number and split it into two equal halves -- so spotting that halving pattern down the table fills every blank, and the bar diagram makes the equal pieces visible.

3 · Execute2 carry out the plan

1Row 2: halve 2000

#5 Look for a Pattern 3.NBT.A.2

Row 2 splits each 2000 into two equal numbers. Half of 2000 is 1000, so every one of the 2 cells in this row is 1000.

1{,}000 + 1{,}000 = 2{,}000

Splitting into two equal parts means each part is half, and half of 2000 is 1000.

2Check the row total

#1 Draw a Diagram 3.OA.A.4

The 2 equal cells of the last row must still cover the whole 2000. Adding them gives 2000, so the fill is consistent.

1{,}000 + 1{,}000 = 2{,}000

The whole bar is unchanged, so the equal pieces in any row always re-add to the total.

Answer: Row 2 cells = 1000 (x2) (every row sums to 2000: 1000 + 1000 = 2000)

4 · Reviewdoes it hold up?

Each row totals 2000, and every split is into two equal halves, so the magnitudes halve correctly down the table (2,000 -> 1,000).

Another way: You could divide instead of halving by inspection: 2000 divided by 2, 4, 8, ... gives the same row cells.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 — Adding the equal cells to confirm each split reproduces the total.
3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding the equal addends that make each row sum to the total.

💡Takeaway. Each row just splits the number in half, so 2,000 -> 1,000!

Variant 2 easy

Decompose the number into a sum of two equal numbers and fill in the blanks.

Reading from top to bottom, the table repeatedly splits one number into a sum of two equal numbers.

Row 1: the whole bar holds $1{,}200$ .
Row 2: the $1{,}200$ from Row 1 is split into two equal numbers shown in two cells, and the right cell reads $600$ .

Fill in the blanks so that the numbers in every row add up to $1{,}200$ .

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A table splits 1200 by halving repeatedly down 2 rows. Fill the blank cells so every row still sums to 1200.

Givens

Row 1 holds 1,200 in a single full-width cell.
Each later row splits every cell above into two equal halves.
The table has 2 rows in total.

Unknowns

The blank cells in every split row.

Constraints

Each row must add up to 1200.
Within a row the cells are equal (each split is into two equal parts).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #1 Draw a Diagram

Each row repeats the same rule -- take a number and split it into two equal halves -- so spotting that halving pattern down the table fills every blank, and the bar diagram makes the equal pieces visible.

3 · Execute2 carry out the plan

1Row 2: halve 1200

#5 Look for a Pattern 3.NBT.A.2

Row 2 splits each 1200 into two equal numbers. Half of 1200 is 600, so every one of the 2 cells in this row is 600.

600 + 600 = 1{,}200

Splitting into two equal parts means each part is half, and half of 1200 is 600.

2Check the row total

#1 Draw a Diagram 3.OA.A.4

The 2 equal cells of the last row must still cover the whole 1200. Adding them gives 1200, so the fill is consistent.

600 + 600 = 1{,}200

The whole bar is unchanged, so the equal pieces in any row always re-add to the total.

Answer: Row 2 cells = 600 (x2) (every row sums to 1200: 600 + 600 = 1200)

4 · Reviewdoes it hold up?

Each row totals 1200, and every split is into two equal halves, so the magnitudes halve correctly down the table (1,200 -> 600).

Another way: You could divide instead of halving by inspection: 1200 divided by 2, 4, 8, ... gives the same row cells.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 — Adding the equal cells to confirm each split reproduces the total.
3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding the equal addends that make each row sum to the total.

💡Takeaway. Each row just splits the number in half, so 1,200 -> 600!

Variant 3 easy

Decompose the number into a sum of two equal numbers and fill in the blanks.

Reading from top to bottom, the table repeatedly splits one number into a sum of two equal numbers.

Row 1: the whole bar holds $2{,}400$ .
Row 2: the $2{,}400$ from Row 1 is split into two equal numbers shown in two cells, and the right cell reads $1{,}200$ .

Fill in the blanks so that the numbers in every row add up to $2{,}400$ .

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A table splits 2400 by halving repeatedly down 2 rows. Fill the blank cells so every row still sums to 2400.

Givens

Row 1 holds 2,400 in a single full-width cell.
Each later row splits every cell above into two equal halves.
The table has 2 rows in total.

Unknowns

The blank cells in every split row.

Constraints

Each row must add up to 2400.
Within a row the cells are equal (each split is into two equal parts).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #1 Draw a Diagram

Each row repeats the same rule -- take a number and split it into two equal halves -- so spotting that halving pattern down the table fills every blank, and the bar diagram makes the equal pieces visible.

3 · Execute2 carry out the plan

1Row 2: halve 2400

#5 Look for a Pattern 3.NBT.A.2

Row 2 splits each 2400 into two equal numbers. Half of 2400 is 1200, so every one of the 2 cells in this row is 1200.

1{,}200 + 1{,}200 = 2{,}400

Splitting into two equal parts means each part is half, and half of 2400 is 1200.

2Check the row total

#1 Draw a Diagram 3.OA.A.4

The 2 equal cells of the last row must still cover the whole 2400. Adding them gives 2400, so the fill is consistent.

1{,}200 + 1{,}200 = 2{,}400

The whole bar is unchanged, so the equal pieces in any row always re-add to the total.

Answer: Row 2 cells = 1200 (x2) (every row sums to 2400: 1200 + 1200 = 2400)

4 · Reviewdoes it hold up?

Each row totals 2400, and every split is into two equal halves, so the magnitudes halve correctly down the table (2,400 -> 1,200).

Another way: You could divide instead of halving by inspection: 2400 divided by 2, 4, 8, ... gives the same row cells.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 — Adding the equal cells to confirm each split reproduces the total.
3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding the equal addends that make each row sum to the total.

💡Takeaway. Each row just splits the number in half, so 2,400 -> 1,200!

Variant 4 medium

Decompose the number into a sum of two equal numbers and fill in the blanks.

Reading from top to bottom, the table repeatedly splits one number into a sum of two equal numbers.

Row 1: the whole bar holds $400$ .
Row 2: the $400$ from Row 1 is split into two equal numbers shown in two cells, and the right cell reads $200$ .
Row 3: each number from Row 2 is again split into two equal numbers shown in 4 cells, and the second cell from the left reads $100$ .

Fill in the blanks so that the numbers in every row add up to $400$ .

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A table splits 400 by halving repeatedly down 3 rows. Fill the blank cells so every row still sums to 400.

Givens

Row 1 holds 400 in a single full-width cell.
Each later row splits every cell above into two equal halves.
The table has 3 rows in total.

Unknowns

The blank cells in every split row.

Constraints

Each row must add up to 400.
Within a row the cells are equal (each split is into two equal parts).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #1 Draw a Diagram

Each row repeats the same rule -- take a number and split it into two equal halves -- so spotting that halving pattern down the table fills every blank, and the bar diagram makes the equal pieces visible.

3 · Execute3 carry out the plan

1Row 2: halve 400

#5 Look for a Pattern 3.NBT.A.2

Row 2 splits each 400 into two equal numbers. Half of 400 is 200, so every one of the 2 cells in this row is 200.

200 + 200 = 400

Splitting into two equal parts means each part is half, and half of 400 is 200.

2Row 3: halve 200

#5 Look for a Pattern 3.NBT.A.2

Row 3 splits each 200 into two equal numbers. Half of 200 is 100, so every one of the 4 cells in this row is 100.

100 + 100 = 200

Splitting into two equal parts means each part is half, and half of 200 is 100.

3Check the row total

#1 Draw a Diagram 3.OA.A.4

The 4 equal cells of the last row must still cover the whole 400. Adding them gives 400, so the fill is consistent.

100 + 100 + 100 + 100 = 400

The whole bar is unchanged, so the equal pieces in any row always re-add to the total.

Answer: Row 2 cells = 200 (x2); Row 3 cells = 100 (x4) (every row sums to 400: 200 + 200 = 400; 100 + 100 + 100 + 100 = 400)

4 · Reviewdoes it hold up?

Each row totals 400, and every split is into two equal halves, so the magnitudes halve correctly down the table (400 -> 200 -> 100).

Another way: You could divide instead of halving by inspection: 400 divided by 2, 4, 8, ... gives the same row cells.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 — Adding the equal cells to confirm each split reproduces the total.
3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding the equal addends that make each row sum to the total.

💡Takeaway. Each row just splits the number in half, so 400 -> 200 -> 100!

Variant 5 medium

Decompose the number into a sum of two equal numbers and fill in the blanks.

Reading from top to bottom, the table repeatedly splits one number into a sum of two equal numbers.

Row 1: the whole bar holds $800$ .
Row 2: the $800$ from Row 1 is split into two equal numbers shown in two cells, and the right cell reads $400$ .
Row 3: each number from Row 2 is again split into two equal numbers shown in 4 cells, and the second cell from the left reads $200$ .

Fill in the blanks so that the numbers in every row add up to $800$ .

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A table splits 800 by halving repeatedly down 3 rows. Fill the blank cells so every row still sums to 800.

Givens

Row 1 holds 800 in a single full-width cell.
Each later row splits every cell above into two equal halves.
The table has 3 rows in total.

Unknowns

The blank cells in every split row.

Constraints

Each row must add up to 800.
Within a row the cells are equal (each split is into two equal parts).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #1 Draw a Diagram

Each row repeats the same rule -- take a number and split it into two equal halves -- so spotting that halving pattern down the table fills every blank, and the bar diagram makes the equal pieces visible.

3 · Execute3 carry out the plan

1Row 2: halve 800

#5 Look for a Pattern 3.NBT.A.2

Row 2 splits each 800 into two equal numbers. Half of 800 is 400, so every one of the 2 cells in this row is 400.

400 + 400 = 800

Splitting into two equal parts means each part is half, and half of 800 is 400.

2Row 3: halve 400

#5 Look for a Pattern 3.NBT.A.2

Row 3 splits each 400 into two equal numbers. Half of 400 is 200, so every one of the 4 cells in this row is 200.

200 + 200 = 400

Splitting into two equal parts means each part is half, and half of 400 is 200.

3Check the row total

#1 Draw a Diagram 3.OA.A.4

The 4 equal cells of the last row must still cover the whole 800. Adding them gives 800, so the fill is consistent.

200 + 200 + 200 + 200 = 800

The whole bar is unchanged, so the equal pieces in any row always re-add to the total.

Answer: Row 2 cells = 400 (x2); Row 3 cells = 200 (x4) (every row sums to 800: 400 + 400 = 800; 200 + 200 + 200 + 200 = 800)

4 · Reviewdoes it hold up?

Each row totals 800, and every split is into two equal halves, so the magnitudes halve correctly down the table (800 -> 400 -> 200).

Another way: You could divide instead of halving by inspection: 800 divided by 2, 4, 8, ... gives the same row cells.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 — Adding the equal cells to confirm each split reproduces the total.
3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding the equal addends that make each row sum to the total.

💡Takeaway. Each row just splits the number in half, so 800 -> 400 -> 200!

Variant 6 medium

Decompose the number into a sum of two equal numbers and fill in the blanks.

Reading from top to bottom, the table repeatedly splits one number into a sum of two equal numbers.

Row 1: the whole bar holds $1{,}400$ .
Row 2: the $1{,}400$ from Row 1 is split into two equal numbers shown in two cells, and the right cell reads $700$ .
Row 3: each number from Row 2 is again split into two equal numbers shown in 4 cells, and the second cell from the left reads $350$ .

Fill in the blanks so that the numbers in every row add up to $1{,}400$ .

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A table splits 1400 by halving repeatedly down 3 rows. Fill the blank cells so every row still sums to 1400.

Givens

Row 1 holds 1,400 in a single full-width cell.
Each later row splits every cell above into two equal halves.
The table has 3 rows in total.

Unknowns

The blank cells in every split row.

Constraints

Each row must add up to 1400.
Within a row the cells are equal (each split is into two equal parts).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #1 Draw a Diagram

Each row repeats the same rule -- take a number and split it into two equal halves -- so spotting that halving pattern down the table fills every blank, and the bar diagram makes the equal pieces visible.

3 · Execute3 carry out the plan

1Row 2: halve 1400

#5 Look for a Pattern 3.NBT.A.2

Row 2 splits each 1400 into two equal numbers. Half of 1400 is 700, so every one of the 2 cells in this row is 700.

700 + 700 = 1{,}400

Splitting into two equal parts means each part is half, and half of 1400 is 700.

2Row 3: halve 700

#5 Look for a Pattern 3.NBT.A.2

Row 3 splits each 700 into two equal numbers. Half of 700 is 350, so every one of the 4 cells in this row is 350.

350 + 350 = 700

Splitting into two equal parts means each part is half, and half of 700 is 350.

3Check the row total

#1 Draw a Diagram 3.OA.A.4

The 4 equal cells of the last row must still cover the whole 1400. Adding them gives 1400, so the fill is consistent.

350 + 350 + 350 + 350 = 1{,}400

The whole bar is unchanged, so the equal pieces in any row always re-add to the total.

Answer: Row 2 cells = 700 (x2); Row 3 cells = 350 (x4) (every row sums to 1400: 700 + 700 = 1400; 350 + 350 + 350 + 350 = 1400)

4 · Reviewdoes it hold up?

Each row totals 1400, and every split is into two equal halves, so the magnitudes halve correctly down the table (1,400 -> 700 -> 350).

Another way: You could divide instead of halving by inspection: 1400 divided by 2, 4, 8, ... gives the same row cells.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 — Adding the equal cells to confirm each split reproduces the total.
3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding the equal addends that make each row sum to the total.

💡Takeaway. Each row just splits the number in half, so 1,400 -> 700 -> 350!

Variant 7 medium

Decompose the number into a sum of two equal numbers and fill in the blanks.

Reading from top to bottom, the table repeatedly splits one number into a sum of two equal numbers.

Row 1: the whole bar holds $1{,}600$ .
Row 2: the $1{,}600$ from Row 1 is split into two equal numbers shown in two cells, and the right cell reads $800$ .
Row 3: each number from Row 2 is again split into two equal numbers shown in 4 cells, and the second cell from the left reads $400$ .

Fill in the blanks so that the numbers in every row add up to $1{,}600$ .

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A table splits 1600 by halving repeatedly down 3 rows. Fill the blank cells so every row still sums to 1600.

Givens

Row 1 holds 1,600 in a single full-width cell.
Each later row splits every cell above into two equal halves.
The table has 3 rows in total.

Unknowns

The blank cells in every split row.

Constraints

Each row must add up to 1600.
Within a row the cells are equal (each split is into two equal parts).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #1 Draw a Diagram

Each row repeats the same rule -- take a number and split it into two equal halves -- so spotting that halving pattern down the table fills every blank, and the bar diagram makes the equal pieces visible.

3 · Execute3 carry out the plan

1Row 2: halve 1600

#5 Look for a Pattern 3.NBT.A.2

Row 2 splits each 1600 into two equal numbers. Half of 1600 is 800, so every one of the 2 cells in this row is 800.

800 + 800 = 1{,}600

Splitting into two equal parts means each part is half, and half of 1600 is 800.

2Row 3: halve 800

#5 Look for a Pattern 3.NBT.A.2

Row 3 splits each 800 into two equal numbers. Half of 800 is 400, so every one of the 4 cells in this row is 400.

400 + 400 = 800

Splitting into two equal parts means each part is half, and half of 800 is 400.

3Check the row total

#1 Draw a Diagram 3.OA.A.4

The 4 equal cells of the last row must still cover the whole 1600. Adding them gives 1600, so the fill is consistent.

400 + 400 + 400 + 400 = 1{,}600

The whole bar is unchanged, so the equal pieces in any row always re-add to the total.

Answer: Row 2 cells = 800 (x2); Row 3 cells = 400 (x4) (every row sums to 1600: 800 + 800 = 1600; 400 + 400 + 400 + 400 = 1600)

4 · Reviewdoes it hold up?

Each row totals 1600, and every split is into two equal halves, so the magnitudes halve correctly down the table (1,600 -> 800 -> 400).

Another way: You could divide instead of halving by inspection: 1600 divided by 2, 4, 8, ... gives the same row cells.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 — Adding the equal cells to confirm each split reproduces the total.
3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding the equal addends that make each row sum to the total.

💡Takeaway. Each row just splits the number in half, so 1,600 -> 800 -> 400!

Variant 8 hard

Decompose the number into a sum of two equal numbers and fill in the blanks.

Reading from top to bottom, the table repeatedly splits one number into a sum of two equal numbers.

Row 1: the whole bar holds $4{,}800$ .
Row 2: the $4{,}800$ from Row 1 is split into two equal numbers shown in two cells, and the right cell reads $2{,}400$ .
Row 3: each number from Row 2 is again split into two equal numbers shown in 4 cells, and the second cell from the left reads $1{,}200$ .

Fill in the blanks so that the numbers in every row add up to $4{,}800$ .

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A table splits 4800 by halving repeatedly down 3 rows. Fill the blank cells so every row still sums to 4800.

Givens

Row 1 holds 4,800 in a single full-width cell.
Each later row splits every cell above into two equal halves.
The table has 3 rows in total.

Unknowns

The blank cells in every split row.

Constraints

Each row must add up to 4800.
Within a row the cells are equal (each split is into two equal parts).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #1 Draw a Diagram

Each row repeats the same rule -- take a number and split it into two equal halves -- so spotting that halving pattern down the table fills every blank, and the bar diagram makes the equal pieces visible.

3 · Execute3 carry out the plan

1Row 2: halve 4800

#5 Look for a Pattern 3.NBT.A.2

Row 2 splits each 4800 into two equal numbers. Half of 4800 is 2400, so every one of the 2 cells in this row is 2400.

2{,}400 + 2{,}400 = 4{,}800

Splitting into two equal parts means each part is half, and half of 4800 is 2400.

2Row 3: halve 2400

#5 Look for a Pattern 3.NBT.A.2

Row 3 splits each 2400 into two equal numbers. Half of 2400 is 1200, so every one of the 4 cells in this row is 1200.

1{,}200 + 1{,}200 = 2{,}400

Splitting into two equal parts means each part is half, and half of 2400 is 1200.

3Check the row total

#1 Draw a Diagram 3.OA.A.4

The 4 equal cells of the last row must still cover the whole 4800. Adding them gives 4800, so the fill is consistent.

1{,}200 + 1{,}200 + 1{,}200 + 1{,}200 = 4{,}800

The whole bar is unchanged, so the equal pieces in any row always re-add to the total.

Answer: Row 2 cells = 2400 (x2); Row 3 cells = 1200 (x4) (every row sums to 4800: 2400 + 2400 = 4800; 1200 + 1200 + 1200 + 1200 = 4800)

4 · Reviewdoes it hold up?

Each row totals 4800, and every split is into two equal halves, so the magnitudes halve correctly down the table (4,800 -> 2,400 -> 1,200).

Another way: You could divide instead of halving by inspection: 4800 divided by 2, 4, 8, ... gives the same row cells.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 — Adding the equal cells to confirm each split reproduces the total.
3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding the equal addends that make each row sum to the total.

💡Takeaway. Each row just splits the number in half, so 4,800 -> 2,400 -> 1,200!

Variant 9 hard

Decompose the number into a sum of two equal numbers and fill in the blanks.

Reading from top to bottom, the table repeatedly splits one number into a sum of two equal numbers.

Row 1: the whole bar holds $3{,}200$ .
Row 2: the $3{,}200$ from Row 1 is split into two equal numbers shown in two cells, and the right cell reads $1{,}600$ .
Row 3: each number from Row 2 is again split into two equal numbers shown in 4 cells, and the second cell from the left reads $800$ .
Row 4: each number from Row 3 is again split into two equal numbers shown in 8 cells, and the second cell from the left reads $400$ .

Fill in the blanks so that the numbers in every row add up to $3{,}200$ .

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A table splits 3200 by halving repeatedly down 4 rows. Fill the blank cells so every row still sums to 3200.

Givens

Row 1 holds 3,200 in a single full-width cell.
Each later row splits every cell above into two equal halves.
The table has 4 rows in total.

Unknowns

The blank cells in every split row.

Constraints

Each row must add up to 3200.
Within a row the cells are equal (each split is into two equal parts).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #1 Draw a Diagram

Each row repeats the same rule -- take a number and split it into two equal halves -- so spotting that halving pattern down the table fills every blank, and the bar diagram makes the equal pieces visible.

3 · Execute4 carry out the plan

1Row 2: halve 3200

#5 Look for a Pattern 3.NBT.A.2

Row 2 splits each 3200 into two equal numbers. Half of 3200 is 1600, so every one of the 2 cells in this row is 1600.

1{,}600 + 1{,}600 = 3{,}200

Splitting into two equal parts means each part is half, and half of 3200 is 1600.

2Row 3: halve 1600

#5 Look for a Pattern 3.NBT.A.2

Row 3 splits each 1600 into two equal numbers. Half of 1600 is 800, so every one of the 4 cells in this row is 800.

800 + 800 = 1{,}600

Splitting into two equal parts means each part is half, and half of 1600 is 800.

3Row 4: halve 800

#5 Look for a Pattern 3.NBT.A.2

Row 4 splits each 800 into two equal numbers. Half of 800 is 400, so every one of the 8 cells in this row is 400.

400 + 400 = 800

Splitting into two equal parts means each part is half, and half of 800 is 400.

4Check the row total

#1 Draw a Diagram 3.OA.A.4

The 8 equal cells of the last row must still cover the whole 3200. Adding them gives 3200, so the fill is consistent.

400 + 400 + 400 + 400 + 400 + 400 + 400 + 400 = 3{,}200

The whole bar is unchanged, so the equal pieces in any row always re-add to the total.

Answer: Row 2 cells = 1600 (x2); Row 3 cells = 800 (x4); Row 4 cells = 400 (x8) (every row sums to 3200: 1600 + 1600 = 3200; 800 + 800 + 800 + 800 = 3200; 400 + 400 + 400 + 400 + 400 + 400 + 400 + 400 = 3200)

4 · Reviewdoes it hold up?

Each row totals 3200, and every split is into two equal halves, so the magnitudes halve correctly down the table (3,200 -> 1,600 -> 800 -> 400).

Another way: You could divide instead of halving by inspection: 3200 divided by 2, 4, 8, ... gives the same row cells.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 — Adding the equal cells to confirm each split reproduces the total.
3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding the equal addends that make each row sum to the total.

💡Takeaway. Each row just splits the number in half, so 3,200 -> 1,600 -> 800 -> 400!

Variant 10 hard

Decompose the number into a sum of two equal numbers and fill in the blanks.

Reading from top to bottom, the table repeatedly splits one number into a sum of two equal numbers.

Row 1: the whole bar holds $6{,}400$ .
Row 2: the $6{,}400$ from Row 1 is split into two equal numbers shown in two cells, and the right cell reads $3{,}200$ .
Row 3: each number from Row 2 is again split into two equal numbers shown in 4 cells, and the second cell from the left reads $1{,}600$ .
Row 4: each number from Row 3 is again split into two equal numbers shown in 8 cells, and the second cell from the left reads $800$ .

Fill in the blanks so that the numbers in every row add up to $6{,}400$ .

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A table splits 6400 by halving repeatedly down 4 rows. Fill the blank cells so every row still sums to 6400.

Givens

Row 1 holds 6,400 in a single full-width cell.
Each later row splits every cell above into two equal halves.
The table has 4 rows in total.

Unknowns

The blank cells in every split row.

Constraints

Each row must add up to 6400.
Within a row the cells are equal (each split is into two equal parts).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #1 Draw a Diagram

Each row repeats the same rule -- take a number and split it into two equal halves -- so spotting that halving pattern down the table fills every blank, and the bar diagram makes the equal pieces visible.

3 · Execute4 carry out the plan

1Row 2: halve 6400

#5 Look for a Pattern 3.NBT.A.2

Row 2 splits each 6400 into two equal numbers. Half of 6400 is 3200, so every one of the 2 cells in this row is 3200.

3{,}200 + 3{,}200 = 6{,}400

Splitting into two equal parts means each part is half, and half of 6400 is 3200.

2Row 3: halve 3200

#5 Look for a Pattern 3.NBT.A.2

Row 3 splits each 3200 into two equal numbers. Half of 3200 is 1600, so every one of the 4 cells in this row is 1600.

1{,}600 + 1{,}600 = 3{,}200

Splitting into two equal parts means each part is half, and half of 3200 is 1600.

3Row 4: halve 1600

#5 Look for a Pattern 3.NBT.A.2

Row 4 splits each 1600 into two equal numbers. Half of 1600 is 800, so every one of the 8 cells in this row is 800.

800 + 800 = 1{,}600

Splitting into two equal parts means each part is half, and half of 1600 is 800.

4Check the row total

#1 Draw a Diagram 3.OA.A.4

The 8 equal cells of the last row must still cover the whole 6400. Adding them gives 6400, so the fill is consistent.

800 + 800 + 800 + 800 + 800 + 800 + 800 + 800 = 6{,}400

The whole bar is unchanged, so the equal pieces in any row always re-add to the total.

Answer: Row 2 cells = 3200 (x2); Row 3 cells = 1600 (x4); Row 4 cells = 800 (x8) (every row sums to 6400: 3200 + 3200 = 6400; 1600 + 1600 + 1600 + 1600 = 6400; 800 + 800 + 800 + 800 + 800 + 800 + 800 + 800 = 6400)

4 · Reviewdoes it hold up?

Each row totals 6400, and every split is into two equal halves, so the magnitudes halve correctly down the table (6,400 -> 3,200 -> 1,600 -> 800).

Another way: You could divide instead of halving by inspection: 6400 divided by 2, 4, 8, ... gives the same row cells.

Standardsmin grade 3

3.NBT.A.2 Fluently add and subtract within 1000 — Adding the equal cells to confirm each split reproduces the total.
3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding the equal addends that make each row sum to the total.

💡Takeaway. Each row just splits the number in half, so 6,400 -> 3,200 -> 1,600 -> 800!

One number, many addition expressions · 10 practice problems

Generated variants — 10

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Where next?