Grade 2 Number and Operations

2.MD.B.6

About the Math
Preferred Resources
Additional Resources
Independent Work
Assessment

Full Standard

Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.

Learning Target (I can)

Create a number line with whole number intervals (equal spacing).
Represent whole numbers on a number line.
Represent a whole number on two different number lines that have different endpoints (e.g. place 80 on a number line that has endpoints of 0 and 100 and 50 and 100).
Find sums and differences within 100 using a number line.

About the Math

Measure A number line is a useful tool for adding and subtracting whole numbers and fractions. A ruler is a tool built around this concept. This standard should be integrated with computational standards in grade 2. Students should have experiences with an equally partitioned number line before transitioning to an empty (or open) number line.

Create a number line with whole number intervals (equal spacing).

Students should have experiences with an equally partitioned number line before transitioning to an empty (or open) number line.

Represent whole numbers on a number line.

Students should be able to identify and place numbers on a number line with given endpoints. At first, those endpoints should be static, common endpoints such as 0 and 100, 0 and 1,000, or 0 and 50. In time, students should begin to work with number lines using varied endpoints.

Represent a whole number on two different number lines that have different endpoints (e.g. place 80 on a number line that has endpoints of 0 and 100 and 50 and 100).

As students develop an understanding of larger numbers on number lines, we should begin to modify the number lines. Essentially, students need to understand that a number line shows the relationship between numbers. Number lines can have any endpoints. Students should understand that the position of a number changes as the endpoints change. For example, 50 is halfway between 0 and 100 but shifts considerably to the left when those endpoints change to 0 and 1,000 and 50 isn't on a number line with the endpoints of 75 and 90.

Find sums and differences within 100 using a number line.

A number line can be used to add and subtract. Students should first add and subtract with a ticked number line before seeing the relationships between ticked and open number lines. In time, students can then work with open number lines. Also, note that students should be able to add and subtract on a number line with varied endpoints. For example, when solving 43 + 35 students shouldn't have to jump from 0 to 43 before adding on 35. Instead, they should be able to start with 43 on the left endpoint.

Essential vocabulary for this standard includes length, unit, number line, sums, differences, measure, and distance.

Progression of Standard within Grade 2

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Quarter 1	Quarter 2	Quarter 3	Quarter 4
Create a number line with whole number intervals (equal spacing). Represent whole numbers on a number line. Represent a whole number on two different number lines that have different endpoints (e.g. place 80 on a number line that has endpoints of 0 and 100 and 50 and 100). Find sums and differences within 100 using a number line.

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map. Information is not the complete standard.

Grade	Grade 3
This concept is not taught prior to grade 2.	Understand a fraction as a number on the number line (3.NF.2)

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Preferred Tasks

These links provide ideas for lessons connected to this standard. They may support small group instruction or whole group collaborative investigations. They are intended to serve as a starting point for planning.

Represent numbers to 100 on a number line:

What is the Equation? +++
Number Line Solution +++
Label the Stars +++
Frog and Toad on the number line (Illustrative Math)

Represent numbers to 1,000 on a number line:

How Far +++
Place the Number +++
Why Does It Go There? +++

Lesson Seeds (Prompts for Rigor)

Rigorous mathematics instruction balances the teaching and learning of conceptual understanding, procedural understanding, and the application of mathematics standards. Below are prompts for applying rigor in your classroom. They may support small group instruction or whole group collaborative investigations. They are intended to serve as a starting point for planning. See the Increasing Rigor page for more information.

Look at the number line to the right. What numbers could might the letters A, B, C, and D represent? Explain your thinking.

Have students place the number 60 on a number line with endpoints of 50 and 70. Then, have them place the number 60 on a number line with endpoints of 0 and 100. How does changing the endpoints affect where 60 is placed? Why is it not in the same place on each number line?
Give students an empty number line. Provide them with a number (or students can use place value dice or digit cards). Students have to create their own end points and place the number you provided appropriately on the number line.
Give students a number line with endpoints. The student has to determine the midpoint and then choose a number less than/greater than the midpoint and place it appropriately on the number line.
Give students an empty number line with one point plotted somewhere on it, say 78. Ask students to pick and label appropriate end points based on where 78 is located.

+++ Indicates recently created HCPSS instructional tasks. These tasks are provided in Google slides. When selected, a copy of the file is added to your drive for classroom use.

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Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.

Book Title	Grade	Pages
Teaching Student-Centered Mathematics	K-3	231 (Guess and Measure, Activity 8.5) 247 (Personal Benchmarks, Activity 8.9) 229 (Crooked Paths, Activity 8.3) Crooked Paths BLM
Hands-On Standards	1-2	106-107 (Standard Units) 108-109 (Inches and Feet) 110-111 (Choosing a Unit)
Groundworks: Reasoning About Measurement	2	64-70 (Make Two Feet) 83-85 (Who am I?) 56-62 (Make a Yard,Grade 3 book)
Brain-Compatible Lessons for Mathematics	2-3	82-85 (Measuring Tools) 89-91 (Me and My Shadow)

Additional Tasks and Lesson Seeds

These links provide ideas for lessons connected to this standard. They may support small group instruction or whole group collaborative investigations. They are intended to serve as a starting point for planning. [NOTE: NCTM membership required for access to Illuminations lessons.]

cucca

Cupcake Mixup (Utah Core Academy lesson)
What Number Am I? (HCPSS)
Endpoint (HCPSS)
How Far? (HCPSS)
Investigating Number Lines Teacher Directions (HCPSS)
Investigating Number Lines Teaching Resource (HCPSS)
Macaroni Math: Where Will I Land? (NCTM Illuminations lesson plan)
Using the Number Line to Compare (NCTM Illuminations lesson plan)
Additional Number Lines (HCPSS)

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Student-Facing Centers

These links provide online and print resources to engage students during independent or center time. These resources could be used as lesson seeds.

Froggy Jumps of 10 (HCPSS-adapted resource)
Number Line Addition and Subtraction (HCPSS-adapted resource)
Adding on the Number Line (DreamBox tool)
Battleship Number Line (Brain Pop)
Estimate Number on a Number Line (Mathsframe)
Numbers on a Number Line (Ambleside)
Number Line Fill (HCPSS resource)

Independent Practice

These resource sheets can be used for independent practice or homework. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

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Learning Targets

Create a number line with whole number intervals (equal spacing).
Represent whole numbers on a number line.
Represent a whole number on two different number lines that have different endpoints (e.g. place 80 on a number line that has endpoints of 0 and 100 and 50 and 100).
Find sums and differences within 100 using a number line.

Learning targets identify what students should be able to do. The resources below can be used to measure student understanding of the standard. The recording sheet can be used to collect data. The rubric can be applied to any task.

Recording Sheet (docx)

Rubric

Assessment Tasks

These tasks align with the learning targets for the standard. They can be combined with other tasks for extended assessment opportunities. Teachers/students are not expected to complete all these tasks.

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