Lesson Overview & Objective:
Students get a chance to explore attributes of measure by answering the question, "What does it mean to be big?" Students are introduced to such concepts as area and fractions and practice their writing skills with a friendly postcard explaining a mathematical error in measurement.
Students will explore the concept of attribute and learn to define an attribute when measuring. Students will explore the concept of area and work on a basic introduction to fractions using an area model. Students will write a friendly postcard to help explain the concept of attribute.
Common Core Mathematical Practices:
- Construct viable arguments and critique the reasoning of others.
- Students distinguish correct logic or reasoning from that which is flawed, and explain the flaw.
- Students make conjectures and use stated assumptions, definitions, and previously established results in constructing arguments.
- Use appropriate tools strategically.
- Students consider the available tools when solving a mathematical problem.
- Make sense of problems and persevere in solving them.
- Students use concrete objects or pictures to help conceptualize and solve a problem.
- Students can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Writing skills to stress while teaching this lesson:
Idea Development (Writing with a clear, central idea or theme in mind; putting researched ideas into one’s own words)
Word Choice ( Using precise nouns to assist the reader’s understanding; incorporating interesting adjectives into the writing; using strong verbs to keep the sentences interesting.)
Holly's Step-by-Step Teacher Instructions:
- Before reading, I told the students that the book has a problem and they need to listen closely to see if they can solve the problem. Read students How Big Is a Foot? By Rolf Myller up to half-way through the book there are no page numbers in my edition). Stop on the page that asks “Why was the bed too small for the Queen?” Ask the students to individually reflect, then brainstorm answers in partners or groups. It is not necessary to share out as a class, you just want to create interest in the question so it can be referred to later in the lesson.
- Give each student a large piece of construction paper (I prefer black so that it won’t match colors of Post-it® Note-sized templates) and have a set of objects to use for measuring on each table (string, two sizes of Post-it® Note-sized templates, base ten cubes, larger blocks, measuring bears, etc). Ask students to use any object that they wish to answer the question, “How big is your piece of paper?” Don’t clarify what you mean by big, just let them use their own way to determine big.
- On chart paper in the room, ask each student to tell you how big their paper was and record each answer. There should be many different answers; see the chart below. Ask students to consider and then discuss – if we are all measuring equal objects (construction paper), why are all of our answers different? There should be a wealth of answers here, but students should discover that we have to define the attitribute that we are measuring and what attitribute will be measuring it.
- As a class, agree that we will measure the width of the piece of paper, which is an attribute (as is length). Make sure to introduce this mathematical vocabulary with look at, say, read, and demonstrate. I insist that when students give answers to me (or talk with one another), they must use the academic vocabulary.
- At this point, I tell the students that we will be using the square Post-it® Note-sized templates to measure the width of the paper. I ask them first to estimate how many Post-it® Note-sized templates long will it be? Discuss as a class. (This discussion on estimation was excellent. I did a personal think aloud and asked students to grade my estimate, then we discussed. Then I asked them to estimate. ) Next, we discussed- what part of the post-it do we use to measure? We had to discuss using the length of one side as our measurement attribute. We also discussed how we put the Post-it® Note-sized templates along the side (that they have to start at the beginning if we are going to count them up). We also must discuss what happens if Post-it® Note-sized templates don’t fit exactly. Eventually we determine that the width of the paper is about 4 post-it edges. I write on the board: 1 paper width = 4 post-it edges. We can then discuss how tall 2 papers would measure if they were stacked, or three papers.
- I asked the students to estimate the measure of the length of the paper. We discussed reasonable estimates, then the students actually measured the length with the edge of the square post-it.
- Then I asked the students to consider the small post-it. We decided on the attribute of the longest side as the attribute we would use to measure. I asked the students to estimate how many long edges of the small Post-it® Note-sized templates would it take to measure the length of the construction paper. Then we measured the length with the small Post-it® Note-sized templates. Repeat the process with the length of the construction paper. Discuss the relationship with the students. Talk about the question, “Would our answer change if we used the large edge of the small post-it to measure?”
- Extend the students thinking to ask, by using the square Post-it® Note-sized templates, how many would it take to measure the entire area of the paper? Estimate first, then discuss, then have students really measure and fill in the paper. Discuss what attributes we are using to measure area (the whole post-it) and that each measurement item is equal (repeated iterations). Add area to the word list. You can discuss with students how we could use repeated addition and even multiplication to find the area.
- Bring students back to the How Big is a Foot book. So why was the bed so small? Discuss, then finish reading the story.
- What do we use as our standard measures? What do we measure? Discuss metric system and standard and discuss things like temperature, liquid, etc.
- Challenge: Move students into homogeneous groups. Each student group completes one challenge then presents their findings to the class. Make sure to coach students on giving good feedback to the presentations, i.e. is there another way to solve the problem?
- For the students that you can push the farthest, provide 4 objects like a cereal box, a basketball, a rectangular prism that is really heavy, and a large odd shaped item that is empty (see picture at right). Ask them to answer the question on the “Which Item is the Biggest?” handout: Which item is the largest? They fill out their argument sheet together and be ready to present. Sample below; click on it to see it in larger form.
- Once the above-grade-level students present, give them a different set of 4 objects that are all the same height and ask them to fill out the “What Item is the Biggest?” sheet again.
- Other challenge for students above grade level: Ask the students to use their filled in area of construction paper and Post-it® Note-sized templates to figure out how you could cut your paper so that four people will each get an equal share of the paper ((Cut Your Paper Handout, side 2 ). They will also need to fill out their “cut your paper” sheet and be ready to present. After they present, they can write about cutting their paper equally for six people.
- A group at grade level: Ask the students to use their filled in area of construction paper and Post-it® Note-sized templates to figure out how you could cut your paper so that two people will each get an equal share of the paper without folding (Cut Your Paper Handout, side 1). They need to fill out their “cut your paper” sheet and be ready to present their answer. After they present, they can write about cutting their paper equally for four people.
- Have all students write a postcard or friendly letter to the king from the apprentice about what mistake was made when designing the bed and why the apprentice should go free (Blank Postcard Handout).
- Follow-up the lesson by reading The Fattest, Tallest, Biggest Snowman Ever by Bettina Ling or How Tall How Short How Faraway by David Adler and discuss the measurement attributes mentioned in each book.