Download Breakout6_GraphingNumberLineActivity

Breakout 6: Connecting our Thinking / Number Lines
9-12 Breakout
Materials
 Research Article:
Developing Number
Sense on the Number
Line (Jennifer M. Bay)
 Ropes or string for
number lines
 BLM6.1 (one set /
pair)
 BLM6.2 (one /group)
Individual  Class Number Line (15)
 Sticky Notes
Minds On… Create random groups of for Matching Cards Activity (BLM6.2), and introduce
 Paper Clips or Clothes
number line representation.
Pins to attach items to
1. Choose two of the following numbers to create a fraction between 0 and 4.
number lines
2 3 4 5 6 7 8 10 12 15 20 30 40 50 100 1000
 Geometers’ Sketch pad
2.Write your fraction and your name on a sticky note, place on class number line
demos
. This creates a good opportunity to reinforce fraction topics through the number line representation.
 Chart Paper, Markers
-Density of rational numbers, Equivalent fractions are the same number, The whole and portioning,
 Glue or Tape
Strategies for comparing and ordering fractions, Represent magnitude as a length , Unit fractions – why
 Curriculum documents
is 1/7 more than 1/8 , Relational thinking – 3/7 is 3 times 1/720/7 is the same as 2 + 6/7 etc
 Small sticker dots
3. Make groups by dividing number line into sections
(optional – for graphs)
Time Bar:
MO: 30
AC: 70
CO: 20
Learning Goals
1. Investigate meanings and connections associated with fraction as linear
measure.
2. Consider importance of flexibility of fraction models
3. Anchor different models in secondary curriculum applications
4. Explore number lines and their connection to algebraic reasoning
5. Make connections between number lines and graphical representations
Groups of 6  Matching Cards (15)
In pairs group the cards according to fraction meanings, then discuss at your table
Q. Which ones do you think your students would struggle with? Why?
Action!
Groups of 3 - 5  Discussion (30)
Group by course(s) to create group sizes between 3 and 5.
Brainstorm curriculum connections related to fractions. Update curriculum portion
of learning wall with examples / colour codes for different fraction meanings.
Update “tips for secondary teachers” list with related insights
Whole Group  (15)
Show video from KNAER – number line activity (grade 6 class)
Q. What do you notice?
Groups of 3-5  Number Line Activity (15)
Give each group materials for a variable number line (string, tape, sticky notes,
clips)
Group place 0, x, 2x, x/3, x+1, and (x+1)/x on their number lines.
Q. What concepts /ideas does this bring out?
Q. Could this activity be used with students? (Distribute article)
Whole Group  Video (15) (Gap Minder – Babies and Religion)
Q. What is the connection between variable number lines and graphical
representations? Watch the video. Turn and Talk.
Points on the graph represent the relationship between two “quantities”, whose
magnitudes are linear measures. The axes are number lines. The magnitude is
distance from zero. The units are different (variable)
Groups of 6  Activity and Discussion (15)
Groups work through activity BLM6.3, making connections between number lines,
Consolidate expressions, and graphical representations. Show Geometers Sketchpad Demo.
Debrief
Individual  Exit Card (5)
What Ideas do you have about number liens?
What is something you’re still wondering about? Post inquiries on learning wall.
Courses:1D, 1P, 1L/2L,
2P, 2D 3E/4E, 3C/4C,
3M, 3U/MHF, Calculus,
Data
Teachers may notice math
talk, questioning,
partitioning, equivalence,
defining the whole,
justifying, strategies,
conceptual understanding,
teacher questioning
Notice:
1) x, 2x, and x/3 will
always be in the same
relative positions for any
value of x
2) when x+1 is placed, it
determines a value for x.
3) notice that (x+1)/x is
always a bit more than 1.
(how much more?)
6.1 Matching Cards
6.2 Number Line Activity
The purpose of this activity is to make connections between number lines,
algebraic expressions, fractions, functions, and graphical representations.
1. Distribute number lines among group members.
2. Each member of the group picks a value for x between 1 and 5 (could pick
fractions)
3. Each member carefully plots the value of the following expressions on
their personal number line for their value of x.
x, 2x,
x
x 1
, x+1,
3
x
4. Combine your number lines to create a graph of the following functions:
f(x)=x
f(x)=2x
x
f(x)=
3
f(x)=x+1
x 1
f(x)=
x
6.2 (continued) Number Lines
0
0
0
0
0
0
10
10
10
10
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