Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
In second grade, each picture or square on a graph stood for one thing. Third graders move to scaled graphs, where one symbol or one unit on the axis can stand for 2, 5, 10 or another amount. A picture graph of favorite pets might use one paw print for every 5 votes, so 4 paw prints stand for 20 votes. When the key is an even number such as 2 or 4, a half symbol can show half that amount.
Students both build and read these graphs. Building requires choosing a sensible scale, labeling axes, writing a title and making bars or symbol rows that match the data. Reading requires paying attention to the key and the scale. The standard asks students to solve one- and two-step problems from the graph, such as how many more students chose soccer than baseball, or how many fewer chose swimming than the top two sports combined. These questions mix graph reading with addition, subtraction and multiplication, since a row of 6 symbols with a key of 5 means 6 × 5 = 30.
Students count 4 symbols as 4 when each symbol means 5. Make reading the key the first step every time.
A bar halfway between 10 and 20 on a scale of 10 means 15, but students may round to 10 or 20. Practise estimating halfway values.
When drawing a graph, children may number the axis 1, 2, 5, 10. Scales must go up in equal steps.
For how many more questions, some students give the difference in squares rather than in data values. Convert to values using the scale first.
In a picture graph, each star means 4 books. Ella has 6 stars and Noah has 3 stars. How many more books did Ella read than Noah?
Answer: Ella read 12 more books than Noah.
Collect real class data, such as favorite fruits or ways of getting to school, and let groups graph it with different scales. Comparing the same data on a scale of 2 and a scale of 5 shows why the key matters. Graph paper makes bar graphs neat and accurate.
Assessments may ask students to complete a graph from a table, read a value, or answer comparison questions. Two-step questions, such as combining two categories and comparing with a third, are common.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 35 (also accepted: 35 apples)
Each symbol means 5, so 7 symbols mean 7 × 5 = 35 apples.
Answer: C) 35
Halfway between 30 and 40 is 35.
Answer: 9 (also accepted: 9 votes)
24 - 15 = 9 more votes for soccer.
Answer: A) Count by 5s
All the numbers are multiples of 5, and counting by 5s keeps the graph a reasonable height.
Answer: 26 (also accepted: 26 students)
Pizza: 8 × 2 = 16. Tacos: 5 × 2 = 10. Together 16 + 10 = 26 students.
Answer: 31 (also accepted: 31 students)
Red and green combined: 18 + 25 = 43. 43 - 12 = 31 fewer for blue.
Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.
A full lesson with slides, activities and an exit ticket on scaled picture graphs and bar graphs, pitched to grade 3 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 3.MD.B.3 with an answer key, ready in about a minute.
Make a worksheet →Turn scaled picture graphs and bar graphs into a quiz students answer online that marks itself, with a class summary for you.
Build a test →A graph where each symbol or each unit on the axis represents more than one item, such as 1 picture for every 5 pets or a bar axis numbered by 2s.
One- and two-step "how many more" and "how many less" problems using data from scaled bar graphs.