Math Unit:
Net Changes on the Number Line
Theme:
Elevator Explorations
Third Grade
Jill Butterworth, Jane Hahn, Kasi Walker, Kelly Mulvihill
Standards:
· Explore numbers less than 0 by the number line
· Develop fluency in adding, subtracting
Lesson 1: Elevator Trips Up and Down by Jill Butterworth
This lesson starts introducing the number line and net change by connecting it with an elevator and skyscraper in the landmark of 1’s using problem solving skills.
Lesson 2: Many ways to Make One Net Change by Kelly Mulvihill
This lesson builds off the concepts presented in lesson one using multiple representations. It will move to 10’s to become proficient in moving along the number line along with introducing how to make one net change.
Lesson 3: Missing Information Problems by Jane Hahn
The student will explore numbers less than 0 and greater than 0 in intervals of 100. The student will solve equations with missing information using different reasoning and proof methods.
Lesson 4: Connecting to the Number Line by Kasi Walker
This lesson continues with information about the number line from lesson 3. Working with hundreds on the number line is a new concept for third grade, it is important to have more than one way to teach and assess the students understanding of the idea being taught.
Unit Reflection
This unit, Elevator Explorations, is a progression of building knowledge of the number line to reach the landmark of 100s. Elevator Explorations gives students the opportunity to connect real-life experiences of riding an elevator to understanding the number line. Lesson 1 starts by using problem solving skills to determine and introduce the concept of riding an elevator in the landmarks of 1s. Vocabulary used throughout the unit is introduced and then built upon in the remainder of the unit. Lesson 2 builds off the concepts of starting and ending points along with net change that was introduced in the prior lesson. Lesson 2 uses multiple representations to guide students through understanding of moving up and down the elevator in the landmark of 10s. Lesson 3 continues to build on the knowledge presented in the first two lessons by having students determine the missing pieces in the net change formula. Students use the landmarks of 100s by having the starting and ending points and determining the missing number along with the net change. Lesson 4 connects Elevator Explorations to the number line, thus giving the students the opportunity to develop a better understanding of the number line with prior knowledge of the elevator lessons. The students will accomplish an understanding of how to move up and down the number line in the landmarks of 1s, 10s, and 100s. Students also work on their skills of exploring numbers less than 0 on the number line.
Elevator Trips Up and Down
Name: Jill Butterworth
Date of Lesson: 09/21/04
Subject Area/Topic: Math/ Net Changes on the number line
Grade Level: 3rd Grade
Estimated Length: 1 class period
Standards:
· Explore numbers less than 0 by extending the number line and through familiar applications
· Develop fluency in adding, subtracting, multiplying, and dividing whole numbers
Outcomes/Objectives:
· Students will understand the net change of numbers when dealing with numbers in the one’s place value
· Given an example of a skyscraper they will be able to find the net change with whole numbers below and above 0.
Vocabulary: net change, positive, negative, starting and ending place
Materials: sheet of paper or long receipt paper, pencil, and worksheet, pictures of elevator and
skyscraper
Procedure: Each child will draw their own skyscraper to assist them in learning net change. (Pictorial)
ENGAGE: Does any one know what a skyscraper is? Does anybody know what an elevator is?
Show examples.
EXPLORE:
a. Each child needs a piece of paper to draw their skyscraper.
b. Have them draw the picture with 19 floors.
c. Label the floors with different things on them (e.g. art studio, mailroom, parking garage)
d. Have them put the numbers on the number line from -9 to 9.
e. Talk about the different pictures of the skyscraper integration into social studies
f. Possible teacher questions are
· Who has been to a tall building?
· What is the highest and lowest floor you have been to?
EXPLAIN:
a. Students will write on the back of their picture what they think is the purpose of a
skyscraper is.
b. Teacher will answer any questions they have about the concept of a skyscraper and
elevator.
c. Have them start on a floor and then move to another floor to find the net change.
d. Write the changes on the worksheet.
e. Possible teacher question:
· How did you find the net change?
· Does it matter what floor you start on or end on?
f. If necessary, teacher will go further into explaining the purpose of an elevator so
that everyone understands the concept of net change ( introduce it as a mail
delivery person and they have to deliver the mail to different floors but is trying to
see what the difference is when going from floor to floor).
EXPAND:
Students will complete their worksheet that suggests various net changes on the
number line.
a. Have students then get together in pairs to compare the different net changes they
found.
b. Teacher will ask for explanations of what happens when you go through floors and
to give examples of net changes.
EVALUATE:
a. Worksheet ( pp.61)
EXTEND:
a. Go into the ten’s place value with the same basic number line.
b. Where else do we use net change?
REFERENCES:
National Council of Teachers.(2000). Principles and Standards for School Mathematics.
National Council of Teachers of Mathematics. Reston,VA.
REFLECTION:
This is a lesson to teach the basic concept of the number line. It is just an introduction
for later in the week when discussing the number line with the landmark in the
hundreds.
Many ways to Make One Net Change
Kelly Mulvihill
September 28, 2004
Math/Number Line-Net Change
3rd Grade
Estimated Length (2 -1hr class periods)
Standards
· Explore numbers less than 0 by the number line
· Develop fluency in adding, subtracting
· Select, apply, and translate among mathematical representations to solve problems
Objectives
· The main idea: find many ways to make one net change
· Make the same net change in many different ways using positive and negative numbers
· Adding and subtracting a series of integers
Vocabulary
Net Change, starting and ending places
Materials
§ Material box with number lines, paper, rulers, markers, long receipt paper, graph paper, scissors, paper clips
§ Worksheets: Student Sheet 2, Changes Cards, Net Change Cards
§ Overhead transparency of Change Buttons on Elevator and Elevator shafts,
§ Overhead Markers, newsprint 1 for each group, student number line journals
Technology
§ Overhead
§
Engage (the concept)
§ Yesterday we discussed making trips up and down our make believe skyscraper on the elevator. You discussed the starting and ending points along with net change.
§ Have you ever been on an elevator that only stops every ten floors? Well today we are going to ride on an elevator that will only stop every ten floors and we have figure out how to get where we want to go!
§ To gain interest, the class will discuss and label each floor of the elevator shaft transparency. Such as toy store, McDonalds, swimming pool, etc. Each floor will have a different place to visit.
Explore (the concept)
a. On the overhead there will be three problems to discuss in groups about starting and ending point and net change.
b. Students will be encouraged to use mental math, pictures, number lines, or any resources EXCEPT a calculator to determine the answers: Material box with number lines, paper, rulers, markers, long receipt paper, graph paper, scissors
§ 60 – 90 + 30 + 20 (40)
§ 85 - 70 - 20 + 45 (40)
§ 20 + 50 – 80 + 70 – 20 (40)
§ If students have a difficult time determining where to start, ask them what they could use in their material box to represent the elevator shafts.
c. Groups will discuss and record these questions that are listed on the overhead
§ What did you discover about the answers?
§ How did you determine the answers? What did you use?
§ List the similarities and differences between the 3 problems.
§ What way would you design questions to get the same result as above?
d. After groups discussed questions they will individually write and draw pictures in math journal of multiple ways to solve the problems on the overhead (PICTORIAL)
e. Possible Teacher questions
§ How do you explain this to someone who has never seen a number line? (It shows where numbers are in order)
§ What other drawings/representations could you use to show the movement on the number line? (along a street/highway)
EXPLAIN (idea of the concept; term introduction)
a. Teacher will emphasis the vocabulary through questioning and having students give examples on the overhead using a number line
§ Net Change – the answer when moving on the number line
§ Starting Place –the floor we began on
§ Ending Place – the floor we ended on
b. Students will devise three problems with four numbers that result in the same net change with landmarks in the tens in their groups.
c. Each group will receive newsprint and display in writing and drawings the 3 problems to present to the class. (PICTORIAL)
d. Groups will present problems to the class and discuss their different methods of determining the answers through writing and drawing.
e. After presentations and vocabulary introduction students are encouraged to write or draw interesting methods presented by other students to discovering problems, and improve their understanding of net change
f. Possible Teacher questions are
§ Why is the starting place important? (To know where to start counting for net change)
§ Why is the ending place important? (To know where to end counting for net change)
EXPAND (the concept):
a. Students are giving a hand out of Changes Cards, students will mark the entire back of their sheets with a distinctive pattern (stripes, zigzags, blotches, initial patterns) so they can recognize their own cards once they are cut out.
b. Ask students while looking at the page
§ What different numbers are on the cards?
§ How many of each number are there?
§ How many number cards will you have when you cut them out?
c. Each student will cut out their cards and paper clip them to stay together.
d. Remind students from previous lesson about the buttons in real elevators.
§ How do you tell an elevator what floor you want to go to? Use previous lesson’s example of elevator buttons
§ When you get in the elevator, you or the elevator operator pushes the button for that floor.
§ The buttons in our make-believe skyscraper are different. They are “change” buttons. Instead of pushing the number of the floor where you want to go, you push the amount you want to go up or down. The buttons on your elevator are the same as the Changes Card you cut out.(Discuss that B = negative)
o Show Elevator Panel that has Change buttons (visual demonstration)
o During the following questions: Have students come and show classmates. Class helps guide student assistant, instead of student doing the actions on their own, then explain how it was accomplished.
o If I was on the 30th floor and I pushed -20, where would I end up?
§ Display on Diagram
§ What is the net change?
o To go from the 10th floor to the 40th floor, what button should I push?
§ Display on Diagram
§ What is the net change? ( continue question pattern for remainder of questions)
o What button would we push to go from floor 20 to floor B10?
o To go from B30 to B10?
o If we start at 10 and push 30 where do we end up?
o If we start at 0 and push -30 where do we end up?
e. Now you are going to plan trips on the elevator by using more than one change. Suppose you like to ride around in the elevator and stop at several floors before getting to your destination.
f. Have students guide you through the directions while working at the overhead.
§ Ask students where to place the start label at any floor other than zero.
§ Have a student pick three Changes Cards and read each card one by one and move accordingly
§ Ask students where to place the end label
§ Ask students what the net change is
g. Write the net change on the board and challenge students in their groups to devise ways to make the same net change using three different changes, have students show examples on board