Big Idea 1
Solving Problems with Data

We begin this grade 3 book with a topic that is extremely important to the 21st century but that is often left out because of time constraints. Textbook publishers often place measurement and data at the end of books, but we have chosen to open with this topic to acknowledge its importance. The activities in this big idea give students opportunities to explore and understand their world-inviting them to ask their own questions and discuss the relevance of data. There can be few more critical activities in which students engage as they learn to be mathematically literate citizens.

In the Visualize activity, we invite students to wonder about the lengths of animal tongues, which should be interesting and engaging. Students are also asked to read a bar graph and work to interpret what it is telling them. We have chosen some animals we think students may be curious about. We encourage you to allow students time to investigate and find out more about the animals. As students work to make sense of graphs and data, they will develop quantitative literacy, which is an extremely important attribute. As students read the graph and work to understand what it is telling them, they will need to pay careful attention to the way the vertical axis is numbered. Later in the activity, we provide students with tables of data and ask them to create visual images that communicate the data. This lesson is inspired by a book by Steve Jenkins, Animals by the Numbers. Having this book available for students would be a nice addition to the lesson.

The Play activity provides students an opportunity to use what they learned in the previous lesson as they inspect a graph that has some mistakes. One of the most debilitating ideas for learners is the myth that they always have to be right. Our Youcubed team has worked hard to dispel this myth by communicating the neuroscience which shows that when students are struggling and making mistakes, brain growth occurs. This lesson is a good time to celebrate the value of mistakes and communicate the brain science information that we also share here: https://www.youcubed.org/resource/brain-science/. Students in this lesson are again encouraged to develop quantitative literacy by reading graphs that display data, and noticing and discussing the mistakes in the graph. It is important to embrace the mistakes and talk about mistakes in playful rather than pejorative tones. Students then get the opportunity to make their own mischievous graph where they can try to mislead their peers with a display that contains mistakes. We think students will love playing Inspector Graph-It.

In the Investigate activity, students investigate a real question about the most common car color in their area. They will pose the question and determine together a data collection plan. Later they will take the data and interpret it to answer the question about car color. This provides an opportunity for students to think about a real question and also consider together why this could be useful information. The extension in this activity is worth the extra days. Students have an opportunity to ask their own questions and collect data. An important goal for us as mathematics educators is to give students opportunities to act with agency-to use their own thoughts and ideas as they work mathematically. It is very helpful to give students opportunities to ask their own questions-instead of only answering questions that have been given to them. When students ask their own questions of data, we achieve both of these goals.

Jo Boaler

Tongues, Tails, and in Between

Snapshot

Students investigate a graph of the lengths of different animals' tongues to develop ways of interpreting data displays, with a focus on reading a scaled axis. Then students choose a set of animal measurement data and create their own data displays to compare and discuss.

Connection to CCSS

3.MD.3

3.NBT.2, 3.NF.1, 3.OA.3

Agenda

• Copies of the Animal Tongue Lengths graph, one per partnership
• Optional: 1" grid paper (see appendix)

• Animal Data Tables, copied and cut into quarters to provide choices for partners
• Make available: 1" grid paper (see appendix), colors

To the Teacher

In this lesson, which can extend across two days, students begin to think about how data can be visual, and the relationship between data and displays. As adults we often have a great deal of comfort with the kinds of data displays used in third grade, and understanding these images comes quickly. But for children, these images don't immediately make data obvious; it takes experience interpreting data displays to become fluent in this visual form of reading. This lesson is designed to give students the opportunity to read displays without the need to answer particular questions imposed from the outside. Instead, we hope to inspire wonder. The bar graph we've constructed to launch this lesson, based on the beautiful data in Steve Jenkins's book Animals by the Numbers, is intended to be intriguing and to get students wondering about the data and the unusual animals it represents. If students want to find pictures of these animals or investigate in other ways, we encourage you to support their curiosity. If you have access to Animals by the Numbers, we encourage you to make this book available to students to explore the many creative ways Jenkins displays and communicates data.

The graph poses a mathematical challenge important for students to grapple with. The vertical axis is scaled in increments of 5, rather than one, and not all of the data falls neatly into multiples of 5. Students need to attend to these increments to measure the length of a bar, and they will need to think proportionately to estimate how long a tongue might be that falls between two increments. Encourage students to make their thinking about these estimates public and discuss which inferences are reasonable and which are not convincing. Several mathematical concepts intersect when students are doing this work, and it is useful to bear in mind all that students are working to integrate. Students need to think in terms of equal groups and skip counting to interpret (and construct) the scaled axis; they need to be thinking about differences on a scale to interpret comparisons; they need to interpret the axis as a number line and think fractionally about the values between increments. Any one of these concepts could provide productive struggle for students as they work first to interpret and then to construct graphs.

Activity

Launch

Launch this lesson by showing students the Animal Tongue Lengths graph on a projector. Ask students what they notice in the graph, or, What does this image show? Give students a few moments to turn and talk to a partner about the graph. Collect from students a few of their observations about the graph. Encourage students to come up to the graph to point out the specific features or data points they notice. Press students to explain any inferences they have made. For instance, students might infer that one animal's tongue is longer than another. You'll want to ask students to point out the specific feature of the graph that communicates that idea. Students might connect a bar with an animal's name or with a measure on the vertical axis. Be sure to probe how they made this connection. Use this brief discussion to encourage students to notice details and make their reasoning public before sending them off to make observations with a partner. Tell students that today they will be exploring this graph and trying to figure out all it is telling us.

Animal Tongue Lengths

Explore

Students work in partners to make observations about the Animal Tongue Lengths graph. Provide each partnership with a copy of the graph. Students record their observations directly on...