Numeracy Development Talk, Tasks, and Practice
Integers
NDT 6.1 A1
Measure to Represent Integers on Number Lines
Numeracy Objectives
This Numeracy Development Talk targets the following essential concepts and strategies:
The value of a tick mark or point on a number line represents its distance and direction from zero.
Measurement bars are used to measure distance and label points on number lines.
Reflecting a positive number across the tick mark for zero generates the opposite negative number, where both numbers are the same distance from zero.
Numbers with no (+/–) sign are positive and measured to the right of zero.
Numbers with a (–) sign are negative and measured to the left of zero.
Numeracy Resources
The following resources are available for this talk:
Numeracy Development Talk — Video
NDT Video 6.1 A1 — Measure to Represent Integers on Number Lines
NLMT — Video Challenges
Use the online interactive Number Line Measurement Tool [NLMT] to complete each Challenge in the Numeracy Development Talk — Video.
NLMT Challenge 2: Measure to label the value of points on a number line
NLMT Challenge 3: Measure to the left of zero to label points for negative integers
Additional Challenges:
NDT Video with Captions
Video Overview and Instructional Notes
The Video Overview and Instructional Notes outline the instructional highlights of this Numeracy Development Talk and list the essential strategies and concepts that are introduced or reviewed. In addition, video pause points with instructional notes identify important representations, strategies, and concepts and offer suggestions for leading the group Challenge discussions with students.
VOIN for Numeracy Development Talk 6.1 A1
Click on the image to download a PDF.
Materials List for Number Line Talk
Measurement Tool Options
The group Challenges in this Numeracy Development Talk can be implemented using one of the following manipulative resources:
Foam Magnetic Measurement Bar Kit for a classroom whiteboard
Note: If this is the student's first introduction to measurement strategies on a number line, it is recommended that teachers use magnetic measurement bars (foam or printable) on a whiteboard to facilitate this NLT. This will provide students with a concrete experience with measurement strategies.Printable Magnetic Measurement Bar PDF for a classroom whiteboard
Click on this link to download and print this PDF for the Printable Magnetic Measurement Bars.Online interactive Number Line Measurement Tool
Click on this link to learn more about how to use the NLMT to facilitate a Number Line Talk.
NDT Materials List
The following number line segments and measurement bars are needed if you are using a classroom whiteboard to conduct the group Challenges in the NDT:
Conceptual Overview
This Numeracy Development Talk reviews the use of measurement bars to plot and label points on number lines. A significant number of students entering middle school ignore distance when labeling tick marks on number lines. This talk allows teachers to review a set of essential number line measurement strategies. Then, students apply these straightforward strategies to plot and label positive and negative integers on number lines.
Many students ignore the distance when labeling tick marks and points on number lines. For example, the number lines below are labeled incorrectly. The incorrect strategies used to label these lines include extending patterns such as skip counting, counting by ones, and doubling. For each incorrect strategy, students ignored the distance between zero and 4 on the number line.
For a number line representing positive numbers (whole numbers, fractions, and decimals), the value of a point is its measured distance from zero. Applying this basic rule for number lines, a bar that measures from zero to the point for 4 has a length of 4 and can be called a 4-bar.
To address these students’ misconceptions, this Number Line Talk will demonstrate how measurement bars can be used to introduce the basic measurement strategy for number lines. Then, students can apply these measurement strategies to label and justify the correct values for tick marks and points on number lines.
Next, a blue bar that measures the length of two yellow 4-bars is added to the measurement key for this number line. The length of the blue bar is found by adding the lengths of the two 4-bars to get 4 + 4 = 8.
Blue 8-bars can be used to measure, label, and justify the values of the tick marks to the right of zero on this number line. This is an opportunity to revist the incorrect pattern-based strategies that students used to intitially label the tick marks to emphasize that values of tick marks and points on number lines are based on measurement strategies and not patterning.
Student can use additional measurement bars to apply measurement strategies to label points on a numbe line. They should e encoraged to use multiple strategies such as measuring the distance from zero and nearby labeled tick marks (e.g., measuring a 2-bar to the left of the tick mark for 24 locates the point for 24 - 2 = 22).
Next, students can reflect points representing positive numbers across the tick mark for zero to locate the opposite negative numbers. Emphasize to students that the process of reflection ensures that opposite integers measure the same distance from zero but in opposite directions on the number line.
Notice that measurement bars will be particularly useful when demonstrating that taking the absolute values of opposite numbers results in the same positive number, because distance is always defined as a positive number. Arrows, on the other hand, represent positive and negative numbers because arrows are defined by length (distance) and direction of the arrow.
Practice Pages for this NDT will challenge students to use measurement bar rulers to plot and label integers on number lines.
Finally, students are challenged to use equally spaced tick marks between integer-labeled tick marks to plot and label negative decimals. Notice that one set of measurement bars is positioned below these number lines to emphasize that equally spaced tick marks measure equal distance on the number line.
Professional Learning Video
PL Video NDT 6.1 A1-3 — Review Number Line Measurement Strategies to Plot and Label Integers
PL Video NDT 6.1 A1-3 with captions
Daily Numeracy Development Tasks
Teachers can display a Daily Daily Numeracy Development Task on the whiteboard so students can review and complete the task during a classroom transition. Each task is also available by clicking on a link to the task in the Number Line Measurement Tool (NLMT).
Then, students share strategies for measuring and labeling points on the number line. This brief activity allows teachers to review essential concepts and strategies introduced in the Numeracy Development Talk Video and applied on the NDT Practice Pages.
Daily Numeracy Development Tasks—6.1 A1
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NLMT — Daily Numeracy Development Tasks
Use the online interactive Number Line Measurement Tool to display each task. After students estimate the value of each point on the line, they can use the NLMT to share their measurement strategies with the class.
Practice Pages
Practice Pages challenge students to apply the concepts and strategies that were introduced in the Numeracy Development Talk and reviewed in each Daily Number Line Task.
Measurement-Bar Ruler
Students will use the rulers to measure, plot, and label points on these Practice Pages. A PDF of a set of rulers can be downloaded by clicking on the image of the Ruler PDF below the Practice Pages. Print these rulers using the same printer/copier used to print the Practice Pages. Then, use a paper cutter to cut out and trim the rulers. This process ensures that the printed size of the rulers and Practice Pages is the same so that rulers measure accurately on the Practice Pages.
PDF of Practice Pages — NDT 6.1 A1
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