# Measuring & Comparing the Lengths of Objects

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## Objective

SWBAT make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8) and solve problems involving addition and subtraction of fractions by using information presented in line plots.

#### Big Idea

Students will use a ruler to measure everyday objects. Then, they will compare the lengths of the objects by adding and subtracting.

## Opening

30 minutes

Process Grid

For today's opening, I skipped my regular Number Talk routine. I wanted to review adding and subtracting with fractions, mixed numbers, and whole numbers. Prior to the lesson, I created a process grid on the board so that students could see the relationship between adding and subtracting as well as the connection between the equation and number line model. Here's what the finished product will look like: Adding & Subtracting Process Grid

I invited students to join me on the front carpet with a Student Number Line.

I provided students with the first task, 1/5 + 3/5. Students immediately said, "That's 4/5!" I modeled how to write the equation and responded: Great! We know that 1/5 + 3/5 = 4/5, but can we show our thinking using a visual model, such as a number line?

Students went right to work. It was interesting to see how many students started on 1/5 and took three jumps of 1/5 instead of the other way around: 1:5 + 3:5. I then modeled a student's thinking on the board as students finished.

Task 2: 1  2/5 + 4/5

For 1 2/5 + 4/5, most students started on 1 2/5 and took jumps of 1/5 up to 2 1/5: 1 2:5 + 4:5. We discussed how 4/5 could be decomposed into 3/5 + 1/5. We could then take a jump of 3/5 to get to 2 wholes and then take one more jump of 1/5 to get to 2 1/5. Again, after each task, I modeled a student's thinking on the board within the process grid categories.

When we got to 3 + 4/5, students said, "That's easy!" I knew it would be, but I wanted to make sure that I provided students with the opportunity to add and subtract with whole numbers in order to make connections between adding and subtracting fractions. Here's a student example: 3 + 4:5.

Next, we moved on to subtraction. Again, students quickly provided the solution to the first problem, 3/9 - 1/9, and again, I encouraged precise number line representations. The biggest challenge with the number line is partitioning the whole into equal-sized parts. Ninths and other uncommon fractional parts are much harder than halves and fourths. Here's a student example: 3:9 - 1:9

Task 5: 1  2/9 - 4/9

Students then represented the process of subtracting from a mixed number (1 2/9 - 4/9) on their number lines. We discussed how 4/9 could be decomposed into 2/9 + 2/9. Then, we took away 2/9 to get to 1 whole and another 2/9 to get to 7/9: 1 2:9 - 4:9

Finally, students practiced subtracting a fraction from a whole number: 2 - 1/9. At this point in our fractions unit, most students understand that 9/9 = 1 whole. It didn't take students long to show that 2 - 1/9 would equal 1 8/9: 2 - 1:9

At this point, I knew students were warmed up and ready for the upcoming activities!

## Teacher Demonstration

20 minutes

Goal & Lesson Introduction

To begin the lesson, I explained the goal: Today, we are going to review how to use a ruler to measure to the nearest 1/2, 1/4, and 1/8 an inch. Next, we will measure objects in our classroom and make a line plot. Finally, we will answer addition and subtraction problems using our line plots and measurements!

The Ruler Game

I continued: To review how to read a ruler, we will first use a computer application called, The Ruler Game

At first, I modeled how to use this tool to practice identifying measurements to the nearest 1/2 inch. Then, students went to The Ruler Game site and practiced on their own. During this time, I conferenced with students to ensure understanding: Identifying 1:2 Inch Measurements.

The best part of this activity is that students were given immediate feedback. Students were able to correct misunderstandings right away and they were also given continual feedback when correct.

As students were ready, I showed them how to change the setting to measuring fourths. I loved being able to increase the complexity of this task slowly! Here's an example of a student finding fourths: Finding Fourths

Finally, students changed the setting to measuring eighths. Most students picked eighths up quickly. However, some students needed a little more practice. Here, I support a student with differentiating between the hash marks on the ruler: Finding Eighths.

## Student Practice

60 minutes

Choosing Partners

Picking math partners is always easy as I already have students placed in desk groups based upon behavior, abilities, and communication skills. Before students began working, I asked them to discuss how they would like to support each other today. I gave them many examples: Do you want to take turns talking out loud? Do you want to solve quietly and then check with each other? Or do you want to turn and talk anytime you get stuck? Students always love being able to develop a "game plan" with their partners!

Powerpoint Presentation

To help teach today's lesson and provide students with guided practice, I created a Google Presentation: Measuring Objects. Students copied the presentation, making the document their own. This way, they could make changes to their own document instead of the teacher template. On Slide 1, we reviewed today's goal and students inserted their own names By: "Student Name."

Labeling and Measuring to the Nearest 1/2 Inch

On Slide 2, students placed the fractions on the ruler to identify fractions of an inch. I wanted to make sure students knew where 1/2 and 1 1/2 was located before they applied understanding to measuring objects!

Next, students moved on to Slide 3, where they measured objects (paperclip, crayon, and glue stick) to the nearest 1/2 inch. Here's and example of a student Measuring Objects to the Nearest 1:2 in.

Monitoring Student Understanding

During this time, I conferenced with every group. My goal was to support students by providing them with the opportunity to explain their thinking and by asking guiding questions. I also wanted to encourage students to construct viable arguments by using evidence to support their thinking (Math Practice 3).

1. What did you do first?
2. What do you need to always remember?
3. Does that feel right?
4. Where is 1/4 located? How do you know?
5. What makes more sense to you?
6. Does that always work?

Labeling and Measuring to the Nearest 1/4 Inch

Then, students went to Slide 4 and Slide 5 to label and measure to the nearest fourth inch. Here, Labeling the Ruler, a student did a great job matching each of the fractions with the correct location on the ruler.

Labeling and Measuring to the Nearest 1/8 Inch

Finally, on Slide 6 and Slide 7, students labeled and measured to the nearest eighth inch.

Line Plot & Problem Solving

As students finished slides 6 and 7, I modeled how to complete the line plot and solve a problem using the information displayed in the line plot.

On Slide 8, I showed students how to make multiple copies of the x by "copying" and "pasting." Then, we discussed an appropriate title and x-axis label.

Next, students took a look at the first problem, Slide 9: What is the difference between the glue stick and crayon? We discussed the meaning of difference and what operation we should use (subtraction).

Next, students solved the problem on their white boards using an equation and number line (just like our opening task). When finished, Students Took a Picture of their work on their white boards and inserted the picture into their own presentation.

Once finished with Slide 9, students then completed Slide 10 with their partners. Here's an example of a student showing his work on slide 10: Adding to Solve. I encouraged him to label his answer and to also test his answer by placing a glue stick and paperclip next to each other on a ruler: Confirming Answer.

Completed Work

Some students were successful at completing this project during this time. Others will finish during tomorrow math block. Here's an example of a completed student presentation: Measuring Objects Student Work.