Practice · One number, many addition expressions · Sensim Math

Variant 1 easy answer: Row 2 cells = 1000 (x2) (every row sums to 2000: 1000 + 1000 = 2000)

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 $2{,}000$ .

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

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 $1{,}200$ .

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

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 $2{,}400$ .

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

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 $400$ .

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

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 $800$ .

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

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 $1{,}400$ .

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

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 $1{,}600$ .

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

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 $4{,}800$ .

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 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)

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 $3{,}200$ .

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 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)

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 $6{,}400$ .

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

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