One number, many addition expressions

3.NBT.A.23.OA.A.4 · take · grade 3

Archetype: Decompose a Number into Parts and Factors · step in a 4-type progression

▶ Practice — 10 problems

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 $1400$ .
Row 2: the $1400$ 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 four cells, and the second cell from the left reads $350$ .

Fill in the blanks so that the numbers in every row add up to $1400$ .

Show solution

Understand

A table splits 1400 by halving repeatedly. Row 1 is the whole 1400. Row 2 splits it into two equal cells (right cell 700). Row 3 splits each Row 2 number again into two equal cells (one cell shown as 350). Fill the blank cells so every row still sums to 1400.

Givens

Row 1 holds 1400 in a single full-width cell.
Row 2 has two equal cells and the right cell shows 700.
Row 3 has four equal cells and the second cell from the left shows 350.
From the figure, each row is made of equal-size pieces that together cover the same total width.

Unknowns

The left cell of Row 2.
The three blank cells of Row 3 (the 1st, 3rd, and 4th cells).

Constraints

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

Plan

#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.

Execute

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

Row 2 splits 1400 into two equal numbers. Two equal numbers that add to 1400 are 700 and 700, which matches the given right cell of 700. So the blank left cell is also 700.

700 + 700 = 1400

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

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

Row 3 splits each 700 from Row 2 into two equal numbers. Half of 700 is 350, matching the given cell. So all four Row 3 cells are 350, and the three blanks are each 350.

350 + 350 = 700

Halving again keeps the equal-pieces pattern: 700 becomes 350 and 350.

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

The four equal cells of Row 3 must still cover the whole 1400. Adding the four 350s gives 1400, so the fill is consistent.

350 + 350 + 350 + 350 = 1400

The whole bar is unchanged, so the equal pieces in any row always re-add to 1400.

Answer: Row 2 left cell = 700; Row 3 blanks = 350, 350, 350 (every row sums to 1400: 700+700, and 350+350+350+350).

Review

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

You could divide instead of halving by inspection: 1400 ÷ 2 = 700 for Row 2 and 1400 ÷ 4 = 350 for Row 3, getting the same blanks.

Standards · min 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 1400.

💡 This only needs Grade 3 halving sense: each row just splits the number in half, so 1400 → 700 → 350!