Translate between table and pictograph

3.MD.B.3 · take · grade 3

Archetype: Read and Scale a Data Graph · step in a 21-type progression

The apples harvested at the orchards in Gyeongho's town were surveyed and shown in a table and a pictograph. Complete the table and the pictograph.

Apples Harvested by Orchard (table)

Orchard	Singsing	Manna	Dalkom	Haengbok	Total
Boxes harvested	$780$			$800$	$3000$

Apples Harvested by Orchard (pictograph)

Orchard	Amount
Singsing
Manna
Dalkom	(6 large apple pictures, 9 small apple pictures)
Haengbok

In the pictograph, each large apple picture stands for $100$ boxes and each small apple picture stands for $10$ boxes.

Show solution

Understand

A table and a matching pictograph show apple boxes for four orchards. The table gives Singsing 780, Haengbok 800, and total 3000, with Manna and Dalkom blank. The pictograph's only filled row, Dalkom, shows 6 large apples (100 boxes each) and 9 small apples (10 boxes each). We complete the table, which means finding Dalkom and Manna.

Givens

Table: Singsing = 780, Haengbok = 800, Total = 3000.
Pictograph legend: 1 large apple = 100 boxes, 1 small apple = 10 boxes.
Dalkom row (from figure): 6 large apples and 9 small apples.
The table and pictograph show the same data.

Unknowns

Dalkom's number of boxes and Manna's number of boxes (to complete the table).

Constraints

The four orchard amounts must add to 3000.
Pictograph amounts come from the large/small apple values.

Plan

#15 Organize Information in More Ways · also uses: #7 Identify Subproblems

Translate the pictograph picture into a number (Dalkom), then treat 'find Manna' as the remaining subproblem using the total. This is moving between two representations of the same data.

Execute

#15 Organize Information in More Ways 3.MD.B.3

Dalkom shows 6 large apples and 9 small apples. Each large apple is 100 boxes, each small is 10 boxes: 6 x 100 = 600 and 9 x 10 = 90, so Dalkom = 600 + 90 = 690.

6 \times 100 + 9 \times 10 = 600 + 90 = 690

Turning scaled picture symbols into a count is exactly what a scaled pictograph teaches in Grade 3.

#7 Identify Subproblems 3.NBT.A.2

The four orchards add to 3000. Subtract the three known amounts: 3000 - 780 - 690 - 800 = 730, so Manna = 730.

3000 - 780 - 690 - 800 = 730

Subtracting the known parts from a known total within 1000 is Grade 3 place-value work.

#15 Organize Information in More Ways 3.MD.B.3

Convert each amount back into apples: Singsing 780 = 7 large + 8 small; Manna 730 = 7 large + 3 small; Dalkom 690 = 6 large + 9 small; Haengbok 800 = 8 large.

780{=}7{\cdot}100{+}8{\cdot}10,\ 730{=}7{\cdot}100{+}3{\cdot}10,\ 800{=}8{\cdot}100

Going from a number back to the right count of large and small symbols is the reverse of reading a pictograph.

Answer: Manna = 730 boxes, Dalkom = 690 boxes (Singsing 7 large + 8 small; Manna 7 large + 3 small; Dalkom 6 large + 9 small; Haengbok 8 large)

Review

Add all four: 780 + 730 + 690 + 800 = 3000, which matches the given total exactly, so the table is consistent.

Subproblem order can vary: first find Singsing+Haengbok+Dalkom = 2270, then Manna = 3000 - 2270 = 730 - same result.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading Dalkom from the scaled apple symbols and converting amounts back into symbols.
3.NBT.A.2 Fluently add and subtract within 1000 — Subtracting the known amounts from 3000 to find Manna.

💡 Each big apple is 100 and each little apple is 10 - count them up, then the total fills in the rest!