Create and Interpret Scaled Graphs - 3rd Grade Math

1. Based on the bar graph of favorite ice cream flavors, each square represents 5 votes. Chocolate has 8 squares, Vanilla has 4 squares, Strawberry has 6 squares, and Mint has 3 squares. How many fewer votes did Mint get than Chocolate?
   Answer: 25 votes Chocolate: $8 \times 5 = 40$ votes. Mint: $3 \times 5 = 15$ votes. Difference: $40 - 15 = 25$ votes. Choice A ignores the scale (8 - 3 = 5). Choice B adds the squares (8 + 3). Choice D adds instead of subtracting the totals (40 + 15).
2. A flower shop counted 16 red flowers, 32 blue flowers, 24 yellow flowers, and 40 pink flowers. If you create a scaled picture graph where each flower symbol represents 8 flowers, which color will need exactly 3 flower symbols?
   Answer: Yellow Yellow has 24 flowers, and 24 divided by 8 is 3, so yellow needs exactly 3 symbols, matching choice C. Red has 16 flowers, which needs 2 symbols. Blue has 32 flowers, which needs 4 symbols. Pink has 40 flowers, which needs 5 symbols. Only yellow lands on exactly 3 symbols.
3. Study the scaled bar graph shown. How many fewer cars were in the Red section compared to the total of Blue and Green sections combined?
   Answer: 15 fewer cars in the Red section From the graph: Red = 3 units × 5 = 15 cars, Blue = 4 units × 5 = 20 cars, Green = 2 units × 5 = 10 cars. Blue + Green = 20 + 10 = 30 cars. Difference: 30 - 15 = 15 fewer cars in Red. Choice B adds all sections together. Choice C gives the total of Blue and Green without subtracting Red. Choice D uses an incorrect calculation of the difference.
4. If the Wednesday value was accidentally recorded as double the actual amount, what should the corrected bar height be?
   Answer: The corrected Wednesday bar should be 3 units high The recorded value of 6 is double the actual amount, so dividing 6 by 2 gives the corrected value of 3. Choice B (4) does not relate to halving 6. Choice C (6) is the recorded value, not the corrected one. Choice D (2) matches Thursday's value instead of the corrected Wednesday value.
5. Refer to the bar graph of laps run in gym class. Each square equals 3 laps. Marcus ran 7 squares and Tia ran 4 squares. Marcus's teacher said, 'You need to run 30 laps total this week.' How many more laps does Marcus need to run to reach 30?
   Answer: 9 laps Marcus ran $7 \times 3 = 21$ laps. He needs $30 - 21 = 9$ more laps. Choice B uses Tia's total ($4 \times 3 = 12$). Choice C is Marcus's current total. Choice D subtracts 7 from 30.
6. Based on the scaled bar graph shown, how many more students chose pizza than chose both tacos and burgers combined?
   Answer: 10 students From the graph: Pizza = 6 squares × 5 = 30 students, Tacos = 2 squares × 5 = 10 students, Burgers = 2 squares × 5 = 10 students. Combined tacos and burgers = 10 + 10 = 20 students. Difference: 30 - 20 = 10 students. Choice A incorrectly uses 3 squares for pizza. Choice B adds pizza to tacos and burgers instead of finding the difference. Choice D finds the total of tacos and burgers but doesn't subtract from pizza.
7. Use the table to answer the question. Layla is making a bar graph of the data. She wants each square on the graph to stand for 5 books. How many squares tall should the bar for Mystery books be if there are 35 Mystery books?
   Answer: 7 squares Each square = 5 books, so $35 \div 5 = 7$ squares. Choice A uses the scale value. Choice C subtracts (35 - 5). Choice D adds (35 + 5).
8. Use the bar graph to answer the question. The graph shows the number of books read by four students in September. Each square on the graph represents 4 books. Maya's bar reaches 6 squares and Jordan's bar reaches 3 squares. How many more books did Maya read than Jordan?
   Answer: 12 books Maya read $6 \times 4 = 24$ books. Jordan read $3 \times 4 = 12$ books. The difference is $24 - 12 = 12$ books. Choice A ignores the scale (6 - 3 = 3). Choice B adds instead of multiplying (6 + 3 = 9). Choice D gives only Maya's total.
9. The bar graph shows pencils sold at the school store. Each square = 4 pencils. Monday: 6 squares, Tuesday: 9 squares, Wednesday: 5 squares, Thursday: 7 squares. On Friday, the store sold 20 pencils. How many squares should the Friday bar have on the same graph?
   Answer: 5 squares Each square = 4 pencils, so $20 \div 4 = 5$ squares. Choice A gives the scale value. Choice C subtracts (20 − 4). Choice D uses the pencil count directly, ignoring the scale.
10. Look at the picture graph. If you wanted to change the scale so that the Pet category with the most votes shows exactly 6 symbols, what would the new scale need to be?
    Answer: Each new symbol should represent 5 pets exactly Dogs has the most symbols (6) representing 6 × 5 = 30 pets total. To show 30 pets with exactly 6 symbols: 30 ÷ 6 = 5 pets per symbol. Choice A would require 7.5 symbols for dogs. Choice B would require 5 symbols for dogs. Choice C would require 3.75 symbols for dogs.
11. Refer to the table of pets in Room 12. Sam wants to make a picture graph where each 🐾 symbol equals 3 pets. How many 🐾 symbols should he draw for Dogs, which has 18 pets?
    Answer: 6 symbols Since each symbol equals 3 pets, Sam divides: $18 \div 3 = 6$ symbols. Choice A uses the scale value itself. Choice C subtracts the scale from the total (18 - 3). Choice D adds instead of dividing (18 + 3).
12. The picture graph shows the number of muffins baked each day. Each 🧁 = 8 muffins. Monday shows 3 symbols, Tuesday shows 5 symbols, and Wednesday shows 2 symbols. How many more muffins were baked on Tuesday than on Monday and Wednesday combined?
    Answer: 0 muffins Tuesday: $5 \times 8 = 40$ muffins. Monday + Wednesday: $(3+2) \times 8 = 40$ muffins. Difference: $40 - 40 = 0$. Choice B uses the scale value. Choice C is Tuesday's total. Choice D adds them all (40 + 40).
13. What scale would make the Math bar exactly 4 units tall?
    Answer: Each unit represents 10 students Since the Math bar represents 40 students and must be 4 units tall, each unit must represent 40 divided by 4, or 10 students, so D is correct. Choice A (8 students per unit) would make the bar 5 units tall. Choice B (6 students per unit) would not produce a whole bar height of 4 units. Choice C (5 students per unit) would make the bar 8 units tall.
14. The picture graph shows the number of cans collected by four classes for a food drive. Each 🥫 symbol stands for 10 cans. Mrs. Lee's class has 5 cans, Mr. Park's class has 3 cans, Ms. Ruiz's class has 7 cans, and Mr. Ito's class has 4 cans. How many cans did Ms. Ruiz's class and Mr. Ito's class collect together?
    Answer: 110 cans Ms. Ruiz's class collected $7 \times 10 = 70$ cans. Mr. Ito's class collected $4 \times 10 = 40$ cans. Together: $70 + 40 = 110$ cans. Choice A adds the pictures without using the scale (7 + 4). Choice B gives only Ms. Ruiz's total. Choice D adds all four classes' cans together.
15. The bar graph shows the number of miles four friends biked this week. Each square equals 2 miles. Ava biked 7 squares, Ben biked 5 squares, Carla biked 9 squares, and Dan biked 4 squares. How many more miles did Carla bike than Ben?
    Answer: 8 miles Carla: $9 \times 2 = 18$ miles. Ben: $5 \times 2 = 10$ miles. Difference: $18 - 10 = 8$ miles. Choice A doubles the square difference wrong or ignores scale (9 - 5 = 4). Choice C adds the squares times scale wrong. Choice D adds their totals (18 + 10 = 28).
16. The bar graph shows cupcakes sold at a bake sale. Each square = 6 cupcakes. Vanilla shows 5 squares, Chocolate shows 8 squares, Red Velvet shows 3 squares, and Lemon shows 4 squares. How many cupcakes were sold in total?
    Answer: 120 cupcakes Total squares: $5+8+3+4 = 20$. Total cupcakes: $20 \times 6 = 120$. Choice A gives only the number of squares. Choice B adds squares plus scale. Choice D adds one extra 6.

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