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5548493
The picture graph shows votes for favorite fruits. <table><tr><th>Fruit</th><th>Picture graph</th></tr><tr><td>Apples</td><td>● ● ●</td></tr><tr><td>Pears</td><td>● ●</td></tr><tr><td>Grapes</td><td>● ● ● ●</td></tr></table> Key: ● = \(2\) votes How many students voted for pears?

Hints

- Find the pears row in the picture graph. - Read the key before using the symbols. - Each symbol in that row represents the same number of votes.

Solution

1. The pears row has \(2\) symbols. 2. Each symbol represents \(2\) votes. 3. The pears row represents \(2 \times 2 = 4\) votes.

Answer

\(4\) students voted for pears.
5548503
A picture graph records the number of stickers collected in three colors. <table><tr><th>Color</th><th>Picture graph</th></tr><tr><td>Red</td><td>★ ★</td></tr><tr><td>Blue</td><td></td></tr><tr><td>Green</td><td>★ ★ ★</td></tr></table> Key: ★ = \(3\) stickers Which color has a value of \(0\)? How many green stickers are shown?

Hints

- A category with no symbols represents zero items. - Count the symbols in the green row. - Apply the key to the green row.

Solution

1. The blue row has no symbols, so it represents \(0\) stickers. 2. The green row has \(3\) symbols. 3. Each symbol represents \(3\) stickers, so \(3 \times 3 = 9\) green stickers are shown.

Answer

Blue has \(0\) stickers. Green has \(9\) stickers.
5402353
A music room counted its rhythm instruments. <table><thead><tr><th>Instrument</th><th>Number</th></tr></thead><tbody><tr><td>Drums</td><td>\(12\)</td></tr><tr><td>Shakers</td><td>\(18\)</td></tr><tr><td>Triangles</td><td>\(9\)</td></tr><tr><td>Wood blocks</td><td>\(15\)</td></tr></tbody></table> A scaled picture graph uses the key “one music-note symbol represents \(3\) instruments.” How many symbols should appear in each row?

Hints

- Use the same key for every row of a scaled picture graph. - For each instrument, find how many groups of \(3\) are in its count. - Check that multiplying each symbol count by \(3\) gives the table value.

Solution

1. Divide each count by \(3\), because each symbol represents \(3\) instruments. 2. Drums: \(12 \div 3 = 4\) symbols. 3. Shakers: \(18 \div 3 = 6\) symbols. 4. Triangles: \(9 \div 3 = 3\) symbols. 5. Wood blocks: \(15 \div 3 = 5\) symbols.

Answer

Drums: \(4\) symbols Shakers: \(6\) symbols Triangles: \(3\) symbols Wood blocks: \(5\) symbols
5402513
A scaled picture graph uses the key “one symbol represents \(6\) items.” Three rows represent \(12\), \(18\), and \(30\) items. How many full symbols are needed in each row, and how many symbols are needed altogether?

Hints

- Use the same key value for all three rows. - Find how many groups of \(6\) are in each category total. - Add the three row lengths only after finding each one.

Solution

1. For \(12\) items, use \(12 \div 6 = 2\) symbols. 2. For \(18\) items, use \(18 \div 6 = 3\) symbols. 3. For \(30\) items, use \(30 \div 6 = 5\) symbols. 4. Add the row lengths: \(2 + 3 + 5 = 10\) symbols altogether.

Answer

The rows need \(2\), \(3\), and \(5\) symbols. The graph needs \(10\) symbols altogether.
5402663
A picture graph will show the numbers of reading badges earned in four themes. One symbol represents \(3\) badges. <table><thead><tr><th>Theme</th><th>Badges</th></tr></thead><tbody><tr><td>Robots</td><td>\(0\)</td></tr><tr><td>Animals</td><td>\(9\)</td></tr><tr><td>Space</td><td>\(15\)</td></tr><tr><td>Sports</td><td>\(6\)</td></tr></tbody></table> How many symbols should appear in each row? Explain how the zero category should be shown.

Hints

- Use the same key for every category, including the category with no data. - A zero value does not remove the category from the graph.

Solution

1. Robots: \(0 \div 3 = 0\) symbols. 2. Animals: \(9 \div 3 = 3\) symbols. 3. Space: \(15 \div 3 = 5\) symbols. 4. Sports: \(6 \div 3 = 2\) symbols. 5. The Robots row should keep its label but contain no symbols.

Answer

Robots: \(0\) symbols Animals: \(3\) symbols Space: \(5\) symbols Sports: \(2\) symbols Show the Robots category as a labeled row with no symbols.
5402713
In a picture graph, one symbol represents \(3\) donated board games. A row originally represented \(12\) games. Then \(6\) more games were donated to that category. How many symbols should the updated row contain?

Hints

- Update the data value before changing the graph row. - Use the key to convert the new total into symbols.

Solution

1. The updated data value is \(12 + 6 = 18\) games. 2. Divide by the value of one symbol: \(18 \div 3 = 6\) symbols.

Answer

The updated row should contain \(6\) symbols.
5403003
A picture graph uses one full symbol to represent \(4\) items. Half symbols may be used. How many full symbols and half symbols are needed to represent \(14\) items?

Hints

- Use full symbols for as many groups of \(4\) as possible. - Find how many items remain after the full symbols. - Compare the remainder with the value of a half symbol.

Solution

1. Three full symbols represent \(3 \times 4 = 12\) items. 2. Two items remain, and a half symbol represents half of \(4\), or \(2\) items.

Answer

Use \(3\) full symbols and \(1\) half symbol.
5403593
A picture graph uses the key “one full symbol represents \(6\) items.” Half symbols may be used. How should rows representing \(9\), \(12\), and \(15\) items be shown?

Hints

- Find the value of a half symbol from the full-symbol key. - Use full symbols for groups of \(6\). - Use a half symbol when \(3\) items remain.

Solution

1. A half symbol represents half of \(6\), or \(3\) items. 2. Nine items use \(1\) full symbol and \(1\) half symbol. 3. Twelve items use \(2\) full symbols. 4. Fifteen items use \(2\) full symbols and \(1\) half symbol.

Answer

\(9\): \(1\) full symbol and \(1\) half symbol \(12\): \(2\) full symbols \(15\): \(2\) full symbols and \(1\) half symbol
5403683
A picture graph uses the key “one symbol represents \(6\) items.” Its rows contain \(2\), \(4\), and \(6\) full symbols. What data value belongs with each row?

Hints

- Use the same key for every row. - Multiply each row’s symbol count by \(6\). - Check that larger rows represent larger data values.

Solution

1. Two symbols represent \(2 \times 6 = 12\) items. 2. Four symbols represent \(4 \times 6 = 24\) items. 3. Six symbols represent \(6 \times 6 = 36\) items.

Answer

The rows represent \(12\), \(24\), and \(36\) items.
5403743
A picture-graph row contains \(6\) symbols, with one symbol representing \(5\) items. The row is split into two new categories: the first gets \(2\) of the symbols, and the second gets the other \(4\) symbols. How many items does each new category represent?

Hints

- Apply the same key to each part of the split row. - Check that the two new data values combine to the original row value.

Solution

1. The first category represents \(2 \times 5 = 10\) items. 2. The second category represents \(4 \times 5 = 20\) items. 3. The two values still total \(30\) items, matching the original row.

Answer

The first category represents \(10\) items, and the second represents \(20\) items.
5403973
A picture graph uses the key “one full symbol represents \(6\) items.” One row contains \(2\) full symbols and \(1\) half symbol. Another row contains \(4\) full symbols. What value belongs with each row?

Hints

- Find the value of a half symbol from the key. - Combine the values of the full and half symbols in the first row. - Apply the same full-symbol key to the second row.

Solution

1. A half symbol represents \(3\) items. 2. The first row represents \(2 \times 6 + 3 = 15\) items. 3. The second row represents \(4 \times 6 = 24\) items.

Answer

The rows represent \(15\) items and \(24\) items.
5548513
A class is making a picture graph titled “Recess Equipment Choices” from this table. <table><tr><th>Equipment</th><th>Students</th></tr><tr><td>Balls</td><td>\(20\)</td></tr><tr><td>Jump ropes</td><td>\(10\)</td></tr><tr><td>Chalk</td><td>\(15\)</td></tr><tr><td>Hula hoops</td><td>\(0\)</td></tr></table> Use only whole ★ symbols. Choose the key from these three choices that works for **every** category: ★ = \(2\) students, ★ = \(5\) students, or ★ = \(10\) students. Then write the completed picture-graph row for each category using ★ symbols; write “no symbols” for a zero row.

Hints

- Test each possible key against every nonzero category; the chosen key must allow whole symbols for all rows. - After choosing the key, convert each data value into a number of symbols. - A category with value \(0\) has a labeled row but no symbols.

Solution

1. A key of ★ = \(2\) students cannot show \(15\) students with whole symbols. 2. A key of ★ = \(10\) students also cannot show \(15\) students with whole symbols. 3. Therefore, use ★ = \(5\) students. 4. Balls: \(20 \div 5 = 4\) stars. 5. Jump ropes: \(10 \div 5 = 2\) stars. 6. Chalk: \(15 \div 5 = 3\) stars. 7. Hula hoops: \(0\) students is represented by no symbols.

Answer

Key: ★ = \(5\) students Balls: ★ ★ ★ ★ Jump ropes: ★ ★ Chalk: ★ ★ ★ Hula hoops: no symbols
5548523
A pet survey has these results: dogs \(8\), cats \(4\), fish \(12\). The key is ● = \(4\) votes. Which candidate picture graph represents the data correctly? <table><tr><th>Candidate</th><th>Dogs</th><th>Cats</th><th>Fish</th></tr><tr><td>A</td><td>● ●</td><td>●</td><td>● ● ●</td></tr><tr><td>B</td><td>● ●</td><td>● ●</td><td>● ● ●</td></tr><tr><td>C</td><td>● ● ● ●</td><td>●</td><td>● ● ●</td></tr></table>

Hints

- Translate each data value into a number of symbols using the key. - Check all three categories in each candidate, not just one. - Eliminate a candidate as soon as one row represents the wrong value.

Solution

1. Dogs need \(2\) symbols because \(2\) groups of \(4\) make \(8\). 2. Cats need \(1\) symbol because \(1\) group of \(4\) makes \(4\). 3. Fish need \(3\) symbols because \(3\) groups of \(4\) make \(12\). 4. Only candidate A has row lengths \(2, 1, 3\).

Answer

Candidate A is correct.
5374383
Two classes made separate picture graphs of books they read. <table> <tr><th>Class</th><th>Picture graph</th><th>Key</th></tr> <tr><td>A</td><td>★ ★ ★ ★ ★ ★</td><td>★ = 8 books</td></tr> <tr><td>B</td><td>★ ★ ★ ★ ★ ★ ★ ★ ★</td><td>★ = 6 books</td></tr> </table> Which class read more books? Explain why comparing only the numbers of symbols would be misleading.

Hints

- Read the key for each picture graph before comparing the rows. - Find the number of books represented by each complete row. - Compare the represented data values, not just the numbers of symbols.

Solution

1. Class A has \(6\) symbols with \(8\) books per symbol: \(6 \times 8 = 48\) books. 2. Class B has \(9\) symbols with \(6\) books per symbol: \(9 \times 6 = 54\) books. 3. Class B read \(54 - 48 = 6\) more books. The symbol counts cannot be compared directly because the two graphs use different keys.

Answer

Class B read \(54\) books, which is \(6\) more than Class A's \(48\) books. The symbol counts alone are not comparable because the graphs use different keys.
5384123
The picture graph shows cards in a box. Each symbol represents \(2\) cards. <table><thead><tr><th>Picture</th><th>Symbols</th></tr></thead><tbody><tr><td>Star</td><td>★ ★ ★ ★ ★</td></tr><tr><td>Moon</td><td>● ● ●</td></tr><tr><td>Sun</td><td>☀ ☀ ☀</td></tr><tr><td>Cloud</td><td>☁ ☁ ☁</td></tr></tbody></table> a) How many cards show each picture, and how many cards are there in all? b) Which picture appears most often? c) How many more star cards are there than cards of each other picture?

Hints

- Use the key to find how many cards each symbol represents. - Find each category total before comparing the categories.

Solution

1. Each symbol represents \(2\) cards. 2. Star: \(5 \times 2 = 10\). Moon: \(3 \times 2 = 6\). Sun: \(3 \times 2 = 6\). Cloud: \(3 \times 2 = 6\). 3. The total is \(10 + 6 + 6 + 6 = 28\). 4. The star count is greatest. 5. The difference is \(10 - 6 = 4\).

Answer

a) Star: \(10\), moon: \(6\), sun: \(6\), cloud: \(6\), total: \(28\). b) The star appears most often. c) There are \(4\) more star cards than cards of each other picture.
5402453
In a picture graph, one lantern symbol represents \(4\) lanterns. A row shows \(2\) full symbols and \(1\) half symbol. Omar says the row represents \(8\frac{1}{2}\) lanterns because a half symbol always means one-half of one item. Explain the error and find the row's value.

Hints

- Apply the fraction to the value of one full symbol. - Combine the values of the full and partial symbols.

Solution

1. A half symbol represents half of the key value, not half of one lantern. 2. Half of \(4\) lanterns is \(2\) lanterns. 3. The two full symbols represent \(2 \times 4 = 8\) lanterns, and the half symbol adds \(2\), for a total of \(10\) lanterns.

Answer

Omar used the half symbol incorrectly. The row represents \(10\) lanterns.
5402753
A picture graph must represent the data values \(9\), \(15\), and \(21\) using only full symbols. The possible keys are one symbol represents \(3\) or one symbol represents \(6\). Which key works, and how many symbols are needed for the three rows?

Hints

- Test whether each data value can be divided evenly by a possible key. - The graph cannot use a fractional symbol in this problem.

Solution

1. A key of \(6\) would require half symbols because none of the three values is divisible by \(6\). 2. All three values are divisible by \(3\). 3. The row counts are \(9 \div 3 = 3\), \(15 \div 3 = 5\), and \(21 \div 3 = 7\) symbols.

Answer

Use one symbol represents \(3\). The rows need \(3\), \(5\), and \(7\) symbols.
5402813
In a picture graph, one full symbol represents \(4\) items, and a half symbol represents \(2\) items. a) What data value is represented by \(3\) full symbols and \(1\) half symbol? b) How many full and half symbols are needed to represent \(22\) items?

Hints

- Treat a half symbol as half the value of a full symbol. - For the second part, use as many full groups as possible and then represent any remainder.

Solution

1. Three full symbols represent \(3 \times 4 = 12\) items, and one half symbol represents \(2\) items, for \(12 + 2 = 14\) items. 2. Five full symbols represent \(20\) items, leaving \(2\) items for one half symbol.

Answer

a) \(14\) items b) \(5\) full symbols and \(1\) half symbol
5402833
A picture graph has rows of \(5\), \(7\), and \(9\) symbols with the key “one symbol represents \(2\) postcards.” The graph will be redrawn with the key “one symbol represents \(4\) postcards,” and half symbols may be used. How many full and half symbols should each new row contain so the data stay the same?

Hints

- First use the original key to recover each category value. - Under the new key, each full symbol represents \(4\) postcards and each half symbol represents \(2\). - Check that each new row represents the same number of postcards as before.

Solution

1. The original rows represent \(5 \times 2 = 10\), \(7 \times 2 = 14\), and \(9 \times 2 = 18\) postcards. 2. With the new key, \(10\) postcards need \(2\) full symbols and \(1\) half symbol. 3. Fourteen postcards need \(3\) full symbols and \(1\) half symbol. 4. Eighteen postcards need \(4\) full symbols and \(1\) half symbol.

Answer

Use \(2\) full symbols and \(1\) half symbol; \(3\) full symbols and \(1\) half symbol; and \(4\) full symbols and \(1\) half symbol.
5402893
A picture graph will use one symbol to represent \(4\) craft supplies. The rows should be arranged from the fewest symbols to the most symbols. <table><thead><tr><th>Supply</th><th>Number</th></tr></thead><tbody><tr><td>Clay blocks</td><td>\(20\)</td></tr><tr><td>Ink pads</td><td>\(8\)</td></tr><tr><td>Paper sheets</td><td>\(16\)</td></tr><tr><td>Thread spools</td><td>\(12\)</td></tr></tbody></table> In what order should the rows appear, and how many symbols should each row contain?

Hints

- Convert each data value into symbols before ordering the rows. - Since every row uses the same key, ordering by symbols will also order the data values.

Solution

1. Ink pads: \(8 \div 4 = 2\) symbols. 2. Thread spools: \(12 \div 4 = 3\) symbols. 3. Paper sheets: \(16 \div 4 = 4\) symbols. 4. Clay blocks: \(20 \div 4 = 5\) symbols. 5. This order goes from the fewest symbols to the most symbols.

Answer

Ink pads: \(2\) symbols Thread spools: \(3\) symbols Paper sheets: \(4\) symbols Clay blocks: \(5\) symbols
5403063
The key is missing from a picture graph. A row with \(4\) symbols is known to represent \(28\) items. a) What does one symbol represent? b) How many items would \(6\) symbols represent?

Hints

- Use the known row to recover the value of one equal symbol. - Once the key is known, apply it consistently to the second row.

Solution

1. Divide the row value by its symbols: \(28 \div 4 = 7\) items per symbol. 2. Apply the key to \(6\) symbols: \(6 \times 7 = 42\) items.

Answer

a) One symbol represents \(7\) items. b) Six symbols represent \(42\) items.
5403193
A picture graph uses one full symbol to represent \(2\) items and a half symbol to represent \(1\) item. The three data values are \(5\), \(8\), and \(11\). a) How many full and half symbols are needed for each row? b) How many half symbols are used in the whole graph?

Hints

- Use full symbols for pairs of items. - An odd data value will leave one item for a half symbol.

Solution

1. For \(5\), use \(2\) full symbols and \(1\) half symbol. 2. For \(8\), use \(4\) full symbols and no half symbol. 3. For \(11\), use \(5\) full symbols and \(1\) half symbol. 4. The whole graph uses \(2\) half symbols.

Answer

a) \(5\): \(2\) full and \(1\) half; \(8\): \(4\) full and \(0\) half; \(11\): \(5\) full and \(1\) half b) \(2\) half symbols
5403243
In a picture graph, one full symbol represents \(8\) items. Row A has \(3\) full symbols and \(1\) half symbol. Row B has \(2\) full symbols and \(1\) half symbol. How many items does each row represent, and how many more items are in Row A?

Hints

- Find the value of a half symbol from the full-symbol key. - Convert both rows to data values before comparing them.

Solution

1. A half symbol represents \(4\) items. 2. Row A represents \(3 \times 8 + 4 = 28\) items. 3. Row B represents \(2 \times 8 + 4 = 20\) items. 4. The difference is \(28 - 20 = 8\) items.

Answer

Row A represents \(28\) items. Row B represents \(20\) items. Row A represents \(8\) more items.
5403343
A picture graph uses one symbol to represent \(9\) items. Three categories have \(18\), \(27\), and \(45\) items. a) How many symbols belong in each row? b) How many more symbols does the largest row have than the smallest row? c) How many more items does the largest category have than the smallest category?

Hints

- Convert each data value into symbols with the common key. - Keep the difference in symbols separate from the difference in represented items.

Solution

1. The row counts are \(18 \div 9 = 2\), \(27 \div 9 = 3\), and \(45 \div 9 = 5\) symbols. 2. The symbol-count difference is \(5 - 2 = 3\) symbols. 3. The data-value difference is \(45 - 18 = 27\) items.

Answer

a) \(2\), \(3\), and \(5\) symbols b) \(3\) more symbols c) \(27\) more items
5403393
A picture graph must represent data values of \(16\), \(24\), and \(40\). Compare these two keys: one symbol represents \(4\), and one symbol represents \(8\). Both keys use only full symbols. Which key uses fewer symbols altogether, and how many symbols does it save?

Hints

- Find the row symbol counts under each key. - Compare the total number of symbols, not only one row.

Solution

1. With a key of \(4\), the rows use \(4\), \(6\), and \(10\) symbols, for \(20\) symbols total. 2. With a key of \(8\), the rows use \(2\), \(3\), and \(5\) symbols, for \(10\) symbols total. 3. The key of \(8\) saves \(20 - 10 = 10\) symbols.

Answer

Use one symbol represents \(8\). It uses \(10\) symbols altogether and saves \(10\) symbols compared with the other key.
5403453
A picture graph uses one full symbol to represent \(10\) items. Row A shows \(3\) full symbols and \(1\) half symbol. Row B must represent \(10\) more items than Row A, but the designer says Row B may use only full symbols. Is that possible without changing the key? Explain what must change.

Hints

- Find Row A's data value before deciding what Row B must show. - List the values that can be made with full symbols under the current key. - Decide whether a partial symbol or a different key is needed.

Solution

1. The half symbol represents \(5\) items, so Row A represents \(3 \times 10 + 5 = 35\) items. 2. Row B must represent \(35 + 10 = 45\) items. 3. Full symbols with this key can represent only multiples of \(10\), and \(45\) is not a multiple of \(10\). 4. The key can stay the same only if Row B is allowed to use \(4\) full symbols and \(1\) half symbol. Otherwise, the key must be changed.

Answer

No. Row B must represent \(45\) items, which cannot be shown with full \(10\)-item symbols only. Allowing \(4\) full symbols and \(1\) half symbol makes the row exact.
5403833
A picture graph uses one full symbol to represent \(4\) items and a half symbol to represent \(2\) items. A row is shown with \(1\) full symbol and \(3\) half symbols. a) How many items does the row represent? b) Rewrite the row using the fewest symbol pieces.

Hints

- Convert every symbol piece into its item value. - Look for pairs of half symbols that can be replaced by a full symbol.

Solution

1. The row represents \(4 + 3 \times 2 = 10\) items. 2. Two half symbols can be replaced by one full symbol. 3. The shortest equivalent row uses \(2\) full symbols and \(1\) half symbol.

Answer

a) \(10\) items b) \(2\) full symbols and \(1\) half symbol
5403873
A display board has room for at most \(12\) picture-graph symbols altogether. The data values are \(8\), \(12\), and \(20\). Compare the keys “one symbol represents \(4\) items” and “one symbol represents \(2\) items.” Which graph fits the board?

Hints

- Find the total symbol count produced by each key. - Compare each total with the board's limit.

Solution

1. With a key of \(4\), the rows need \(2\), \(3\), and \(5\) symbols, for \(10\) symbols altogether. 2. With a key of \(2\), the rows need \(4\), \(6\), and \(10\) symbols, for \(20\) symbols altogether. 3. Only the \(10\)-symbol graph fits the \(12\)-symbol limit.

Answer

Use the key one symbol represents \(4\) items. That graph uses \(10\) symbols and fits the board.
5404013
A picture graph uses one full symbol to represent \(8\) items. Row A shows \(3\) full symbols. Row B shows \(2\) full symbols and \(2\) half symbols. Which row represents more items, or do they represent the same amount? Explain why counting the number of symbol pieces gives the wrong comparison.

Hints

- Combine half symbols into full-symbol units before comparing the rows. - Distinguish the number of symbol pieces from the amount those pieces represent. - Use the key only after finding each row’s total symbol amount.

Solution

1. Row A has \(3\) full-symbol units and represents \(3 \times 8 = 24\) items. 2. Two half symbols combine to make \(1\) full-symbol unit, so Row B also has \(2 + 1 = 3\) full-symbol units. 3. Row B represents \(3 \times 8 = 24\) items. 4. Row B has more separate pieces, but the pieces combine to the same total symbol amount as Row A.

Answer

The rows represent the same amount: \(24\) items each. Counting symbol pieces is misleading because two half symbols equal one full symbol.
5404163
A scaled picture graph uses the key: one visitor symbol represents \(10\) visitors. Monday has \(3\) full symbols and \(1\) half symbol. Tuesday has \(2\) full symbols. How many more visitors would Tuesday need so its row represents the same number as Monday's row?

Hints

- Find the value of the half symbol from the key. - Translate each row into a number before comparing them.

Solution

1. Monday's row represents \(3 \times 10 + 5 = 35\) visitors. 2. Tuesday's row represents \(2 \times 10 = 20\) visitors. 3. Tuesday needs \(35 - 20 = 15\) more visitors.

Answer

Tuesday would need \(15\) more visitors.
5404253
A picture graph uses one key for every row. Row A has \(4\) full bird symbols and is labeled \(24\) sightings. Row B also has \(4\) full symbols but is labeled \(30\) sightings. Can both rows be correct? Explain, and correct Row B while keeping Row A unchanged.

Hints

- Use Row A to recover the graph's key. - Equal numbers of full symbols must represent equal data values under one key.

Solution

1. Row A shows that one full symbol represents \(24 \div 4 = 6\) sightings. 2. With the same key, \(4\) symbols in Row B would also represent \(24\) sightings, not \(30\). 3. To represent \(30\) sightings with a key of \(6\), Row B needs \(30 \div 6 = 5\) full symbols.

Answer

Both rows cannot be correct with one key. Keep the key one symbol represents \(6\) sightings and change Row B to \(5\) full symbols.
5404303
A scaled picture graph uses the key “one ballot symbol represents \(5\) votes.” A row has \(6\) full symbols. After \(10\) votes are disqualified, a student erases \(10\) symbols. Explain the student's unit error and give the correct number of symbols for the row.

Hints

- Keep track of whether each number counts votes or symbols. - Use the key to convert the removed votes into a number of symbols.

Solution

1. The student treated votes and symbols as though they were the same unit, but each symbol represents \(5\) votes. 2. Removing \(10\) votes means removing \(10 \div 5 = 2\) symbols. 3. The corrected row has \(6 - 2 = 4\) full symbols.

Answer

The student erased symbols instead of converting the \(10\) votes with the key. The row should have \(4\) full symbols.
5404343
The key on a picture graph is smudged. It says that one full symbol represents either \(4\) items or \(6\) items. Row A has \(4\) full symbols and is labeled \(24\) items. Row B has \(2\) full symbols and \(1\) half symbol and is labeled \(15\) items. Which key is correct? Show that it works for both rows.

Hints

- Use the row with only full symbols to test the two possible keys. - After choosing a key, find the value of a half symbol. - Verify that the same key matches the second row’s label.

Solution

1. Row A has \(4\) full symbols and represents \(24\) items, so one full symbol must represent \(24 \div 4 = 6\) items. 2. With a key of \(6\), a half symbol represents \(3\) items. 3. Row B then represents \(2 \times 6 + 3 = 15\) items, matching its label. 4. A key of \(4\) would make Row A represent only \(16\) items, so it cannot be correct.

Answer

The correct key is one full symbol represents \(6\) items. Row A gives \(4 \times 6 = 24\), and Row B gives \(2 \times 6 + 3 = 15\), so the key works for both rows.
5404433
A scaled picture graph uses the key: one mask symbol represents \(6\) masks. One row has \(4\) full symbols and \(1\) half symbol. A second category has \(9\) more masks. How many full symbols should represent the second category?

Hints

- Find the value of the half symbol. - Convert the first row to a number of masks. - Add the stated difference, then use the key to convert back to symbols.

Solution

1. A half symbol represents \(6 \div 2 = 3\) masks. 2. The first row represents \(4 \times 6 + 3 = 27\) masks. 3. The second category has \(27 + 9 = 36\) masks. 4. Convert back to symbols: \(36 \div 6 = 6\).

Answer

The second category should be represented by \(6\) full symbols.
5404523
A scaled picture graph uses the key: one kite symbol represents \(6\) kites. The first row has \(2\) full symbols and \(1\) half symbol. The second row has \(4\) full symbols, and the third row has \(3\) full symbols. How many kites are represented altogether?

Hints

- Use the key to find the value of a half symbol. - Convert each row into a number of kites. - Add the three row values.

Solution

1. The first row represents \(2 \times 6 + 3 = 15\) kites. 2. The second row represents \(4 \times 6 = 24\) kites. 3. The third row represents \(3 \times 6 = 18\) kites. 4. Add the row values: \(15 + 24 + 18 = 57\).

Answer

The graph represents \(57\) kites altogether.
5404553
A scaled picture graph uses the key: one flag symbol represents \(4\) flags. The shorter row has \(3\) full symbols, and the longer row has \(6\) full symbols. a) How many flags does each row represent? b) How many more flags does the longer row represent?

Hints

- Use the key with the number of symbols in each row. - Convert both rows to flag counts before comparing them. - Subtract the smaller count from the larger count.

Solution

1. The shorter row represents \(3 \times 4 = 12\) flags. 2. The longer row represents \(6 \times 4 = 24\) flags. 3. Find the difference: \(24 - 12 = 12\) flags.

Answer

a) Shorter row: \(12\) flags; longer row: \(24\) flags b) \(12\) more flags
5404583
A scaled picture graph uses the key: one canoe symbol represents \(10\) canoes. One row has \(4\) full symbols and \(1\) half symbol. Another row has \(2\) full symbols and \(1\) half symbol. If the categories are combined, how many full symbols should the combined row have?

Hints

- Convert each mixed-symbol row to its data value. - Add the category values before using the key to build the new row.

Solution

1. The first row represents \(4 \times 10 + 5 = 45\) canoes. 2. The second row represents \(2 \times 10 + 5 = 25\) canoes. 3. The combined value is \(45 + 25 = 70\) canoes. 4. The combined row needs \(70 \div 10 = 7\) full symbols.

Answer

The combined row should have \(7\) full symbols.
5404603
A scaled picture graph uses the key: one leaf symbol represents \(8\) leaves. A row has \(5\) full symbols. The data for that category are reduced to exactly half of the original amount. How many full and half symbols should the new row show?

Hints

- Find the original data value before reducing it. - Use full symbols first, then decide whether a half symbol is needed for the remainder.

Solution

1. The original row represents \(5 \times 8 = 40\) leaves. 2. Half of \(40\) is \(20\) leaves. 3. Two full symbols represent \(16\) leaves, and one half symbol represents \(4\) leaves. 4. The new row should show \(2\) full symbols and \(1\) half symbol.

Answer

The new row should have \(2\) full symbols and \(1\) half symbol.
5404643
A scaled picture graph uses the key: one badge symbol represents \(4\) badges. The three rows show \(2\) full symbols and \(1\) half symbol, \(3\) full symbols and \(1\) half symbol, and \(4\) full symbols and \(1\) half symbol. How many full symbols and half symbols appear altogether, and how many badges do all three rows represent?

Hints

- Count full symbols and half symbols separately across the rows. - Convert the combined symbol amounts using the graph's key.

Solution

1. The rows contain \(2 + 3 + 4 = 9\) full symbols. 2. Each row contains one half symbol, so there are \(3\) half symbols altogether. 3. The \(9\) full symbols represent \(9 \times 4 = 36\) badges. 4. Each half symbol represents \(2\) badges, so the \(3\) half symbols represent \(3 \times 2 = 6\) badges. 5. Altogether, the rows represent \(36 + 6 = 42\) badges.

Answer

There are \(9\) full symbols and \(3\) half symbols. Together, the rows represent \(42\) badges.
5548533
An incomplete picture graph represents \(40\) bicycles altogether. <table><tr><th>Color</th><th>Picture graph</th></tr><tr><td>Red</td><td>★ ★ ★</td></tr><tr><td>Blue</td><td>★ ★ ★ ★</td></tr><tr><td>Green</td><td>?</td></tr></table> Key: ★ = \(4\) bicycles How many green bicycles are there, and how many ★ symbols should complete the green row?

Hints

- Use the key to find the data values represented by the red and blue rows. - Subtract those known values from the total of \(40\). - Convert the missing data value back into a number of symbols.

Solution

1. Red represents \(3 \times 4 = 12\) bicycles. 2. Blue represents \(4 \times 4 = 16\) bicycles. 3. The known rows total \(12 + 16 = 28\) bicycles. 4. Green must represent \(40 - 28 = 12\) bicycles. 5. Twelve bicycles require \(3\) symbols because each symbol represents \(4\).

Answer

There are \(12\) green bicycles, so the green row needs \(3\) ★ symbols.
5403493
A picture graph key says one full symbol represents \(4\) items. A row contains \(3\) full symbols but is labeled \(10\) items. Explain why the row and label do not match. Give two possible corrections.

Hints

- Use the key to calculate the value of the symbols already shown. - A valid correction may change either the data label or the symbol display, but they must agree afterward.

Solution

1. Three full symbols represent \(3 \times 4 = 12\) items, not \(10\). 2. One correction is to keep \(3\) symbols and change the label to \(12\) items. 3. Another correction is to keep the label \(10\) and show \(2\) full symbols plus \(1\) half symbol, because \(8 + 2 = 10\).

Answer

The row represents \(12\), not \(10\). Either change the label to \(12\), or change the row to \(2\) full symbols and \(1\) half symbol.
5404383
A scaled picture graph uses the key: one ribbon symbol represents \(8\) ribbons. The green row has \(3\) full symbols and \(1\) half symbol. The blue row represents \(12\) more ribbons than the green row. How many full symbols should the blue row have?

Hints

- Translate the mixed-symbol row into its data value first. - Apply the stated difference before converting the new value back into symbols.

Solution

1. The half symbol represents \(8 \div 2 = 4\) ribbons. 2. The green row represents \(3 \times 8 + 4 = 28\) ribbons. 3. The blue row represents \(28 + 12 = 40\) ribbons. 4. The blue row needs \(40 \div 8 = 5\) full symbols.

Answer

The blue row should have \(5\) full symbols.
5404473
A scaled picture graph uses the key: one drum symbol represents \(4\) drums. All rows together contain the equivalent of \(15\) full symbols. One row containing \(3\) full symbols and \(1\) half symbol is removed. How many drums are represented by the remaining rows?

Hints

- Translate both the complete graph and the removed row into data values. - A half symbol represents half of the key value.

Solution

1. The original graph represents \(15 \times 4 = 60\) drums. 2. The removed row represents \(3 \times 4 + 2 = 14\) drums. 3. The remaining rows represent \(60 - 14 = 46\) drums.

Answer

The remaining rows represent \(46\) drums.
5404503
A picture graph must represent \(28\) postcards. Give two correct row designs: one using the key “one symbol represents \(8\) postcards” with half symbols allowed, and one using a different key so the row uses only full symbols.

Hints

- For the first design, find how much remains after using several full symbols. - A half symbol represents half of the key value. - For the second design, choose a key that divides the total evenly.

Solution

1. With a key of \(8\), three full symbols represent \(3 \times 8 = 24\) postcards. 2. One half symbol represents \(4\) postcards, so \(3\) full symbols and \(1\) half symbol represent \(28\). 3. A different valid key is one symbol represents \(4\) postcards. 4. With that key, \(28 \div 4 = 7\) full symbols represent the data.

Answer

One design uses \(3\) full symbols and \(1\) half symbol with the key “one symbol represents \(8\) postcards.” Another uses \(7\) full symbols with the key “one symbol represents \(4\) postcards.”
5404673
A scaled picture graph uses the key: one marble symbol represents \(8\) marbles. Row A has \(4\) full symbols, and Row B has \(3\) full symbols and \(1\) half symbol. Four marbles are moved from category A to category B. What should the two rows show after the move?

Hints

- Translate each starting row into a data value. - Apply the transfer to both categories, then convert the new values back into symbols.

Solution

1. Row A originally represents \(4 \times 8 = 32\) marbles. 2. Row B originally represents \(3 \times 8 + 4 = 28\) marbles. 3. After the move, category A has \(32 - 4 = 28\) marbles, represented by \(3\) full symbols and \(1\) half symbol. 4. Category B has \(28 + 4 = 32\) marbles, represented by \(4\) full symbols.

Answer

Row A should show \(3\) full symbols and \(1\) half symbol. Row B should show \(4\) full symbols.

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