This collection or resources focuses on third grade standards relating to bar graphs.

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*.

**Pre-Assessment:**

Many teachers begin instruction of new skills with a pre-assessment of some kind. This can take the form of a performance assessment where the child sits one-on-one with the teacher to show what he/she knows, or it can simply be a paper & pencil type of assessment. For this skill, we have created a more traditional type of assessment that you can use. Give these to students before your instruction begins, but be sure to tell them that their answers will only be used to help you know what you need to teach them. (We find that ALWAYS stating this before a pre-assessment alleviates anxiety in students who feel they are supposed to “know” all the answers on tests.) Of course you could also choose to give students a set of data and tell them to create a bar graph. What they create will give you an idea of what they know and don’t know about bar graphs. Yet another idea is to do both.

**Mini-Lessons**:

Below is a list of suggested mini-lessons that could be used for teaching this standard. Of course you would need to use your pre-assessments to determine if they are needed or to decide if other mini-lessons need to be added.

Lesson 1: Start with a Concrete Example – Whenever possible in math, begin with concrete examples and then move to the abstract. Gather four different colors of LEGO blocks. We suggest using Duplo blocks because they are bigger and will be better for display. Be sure you have enough blocks of each color so that all of your students will have the color choice they want. (You don’t want to run out of blue if that seems to be a class favorite.) Have students go pick up their favorite color from tubs in the front of the room. Next, use the *Building Block Data Collection *page provided to record tally marks for each color. Don’t forget to model for the students how to write in the question at the top. For this lesson you could simply write, “What is your favorite color of block?” Then, have students come to the front to record their own tally marks in the correct spaces as the class watches. When this is finished, direct students into color groups and tell them to build a tower by connecting all the blocks on top of one another. When they are finished set the towers side by side at the front of the room for all to see. You now have a concrete bar graph that you can use and refer to throughout the rest of the mini-lessons. Discuss “noticings” on this first day such as the most popular color and the least popular color.

Lesson 2: Data Collection & Introduction to Bar Graphs – Display the data collection page you created from Lesson 1 and together total the tally marks for each color. Tell students that after they collect data for things (perhaps in the form of tally marks) they can then create bar graphs to make the data easier to understand, compare and contrast. Show the *Making a Bar Graph* anchor chart and discuss the parts of a bar graph as well as why each part is important. (We have created one anchor chart with labels indicating the x- and y- axes and one without so that you can choose whether or not you want (or need) your students to know these terms. We also have one in color and one in black & white.)

Lesson 3: Creating a Bar Graph – Now use the data collection page to model for students how to take that information and create a bar graph. Be sure to refer back to the anchor chart to show students how to check that each part is included (title of graph, labels for both axes, labeled categories and numbered tick marks, etc). For this graph you will use our blank graph that has four boxes for the x-axis. *Be sure to tell and show students the blank sheets we provided that contain 3 and 5 x-axes boxes as well because they may need to use one of those for their small group task later. You might also want to emphasize that any number of categories can be used for this, although you would discourage too many as the graph might get difficult to read. *

Lesson 4: Using the Graph to Ask & Answer Questions About the Information – Once you have constructed your graph with the class, you want to teach them how to answer and ask questions about the information provided. Comparing and contrasting the information on the graph is an important part of the reason people create graphs, and being able to ask and answer questions is key in understanding the information. For this lesson, we have created a set of cards that have questions. Display the LEGO graph you created and have volunteers choose cards, read the questions aloud and then discuss the answers together.

**We have provided an Editable Blank Box page with the same design as ours in case you want to type some additional questions for your LEGO graph or create some specific questions for a bar graph you will use at a center.

Lesson 5: Creating Scaled Bar Graphs – Students need to understand that squares (or heights) on a bar graph might sometimes indicate more than one “vote” or number. Sometimes each jump on the bar might represent 2 or 5 “votes” if the information being represented contains larger numbers. Display our bar graph examples and discuss how how they are the same and how they are different from the LEGO graph you made. Be sure to draw their attention to the bottom where the graph indicates how many “votes” each square on the graph is worth and how this affects the labeling of the y-axis. Pose some questions and use the answers your students give to gauge their understanding.

For a center activity we have created a collection of cards that contain data for graphs. Place the cards and copies of the blank graphs at the center. Students choose a card and create a graph to match the data presented on the card. For some differentiation you can choose the cards that specific students are to use. Some contain numbers, some contain tally marks, some have three, four or five categories to include and some indicate that the graphs need to be scaled graphs.

**Small Group Task:**

We love using cooperative groups in math whenever possible. Assign small groups of three or four students or let your students choose their own groups. Provide data collection sheets and class lists to each group. Also give each of the groups a poster sized piece of paper. This can be plain, graph or lined paper depending on your students and their needs. The task will be to brainstorm a question and some possible answer choices for which to poll the class. The groups will use the class list to make sure they have asked each student in the class the question and then record the data on the data collection page. It will then be the group’s job to create a bar graph that matches their data to present to the rest of the class.

**Guided Small Group Activity** – For students who need additional practice with creating bar graphs, you will want to pull them together in small guided groups to address misconceptions they may have. Meet with these groups for an additional three or four days to help them work through the data collection & graphing process again in a more intimate setting. For this, we suggest an activity similar to the more concrete example described above using the LEGO blocks. Give each of the students in your group 1/4 cup of Fruit Loops (or similar colored cereal). With your guidance, have each sort his/her cereal by color and fill out the data collection sheet. After checking these for accuracy, give students a blank graph to work on. When these are completed you can begin to have discussions with students about their graphs. You can have them answer questions you pose about the data and also help them to brainstorm questions to write about the data in their graphs. (They can share these with peers for extra practice in answering questions about bar graphs.) Be sure to pull groups of students who need additional instruction for the more complex graphs as well. You can use the same type of activity where they are using cereal (or something similar), but the graphs they create will show the difference in marking on the y-axis.

**Final Assessment:**

We have created a paper & pencil assessment that mirrors the pre-assessment we made if you want your assessments to be the same, however you might choose to have your students do a performance assessment to see what their new level of understanding might be. Give them the data collection page and provide copies of the various blank bar graphs. Have them brainstorm a question, collect data and create a graph that matches the data – much the same as the small group task described above.

**Bar Graph Collection Download all of the printables for the following activities here.**

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