The Number Line in the Common Core

Classroom Activities

Activity One - Cuisenaire Rod Exploration

Objective:  Students will recognize the connection between length and number.

Procedure: Students will work with Cuisenaire rods to match and compare a unit length (the white rod/cube) with rods of other lengths.  Through practice and guidance, students will see that a number of unit lengths are assembled to match another rod and the number of units used to match it is the length of the rod.  Placing rods end to end creates a new length (addition) and comparing two different lengths by putting rods side by side illustrates the difference (subtraction).

Mini-lesson: Present the Cuisenaire rods to the students. Explain that these rods belong together in a set and they each have their own color name.  Show that the rods are designed to compare length by creating the “staircase” arrangement, in the following order:

White 

Red 

Light green 

Purple 

Yellow

Dark green

Black

Brown

Blue

Orange

Prepare bins of Cuisenaire rods, enough for each student to have access to a complete set of rods plus a number of extra white rods.  Group students in small groups of 2 or 3 for the activity and practice.  Allow students recreate the staircase and spend some time exploring with the materials. After a few minutes, students should be ready for guided instruction.

Students, with their partners, will show the number lengths of the red rod up to the orange rod by placing the corresponding number of units (white rods) directly next the chosen colored rod, demonstrating the connection between length and number.  What are they noticing as they work together?  Write some of their comments on chart paper or the board.

Allow students to discover combinations of rods with unit measurement as the number. Guiding questions to ask as students explore:  How many units does it take to make this length?  How many more units do we need to make this length? Let’s compare the red and light green.  How are they different? By how much?  Compare two other colored rods and describe what you discover.

Activity Two – Decomposing Base Ten Components

Objective: Students will use base ten blocks to demonstrate the Commutative Rule

Procedure:  Student will move from Cuisenaire rods to base ten blocks, particularly to unit cubes and ten rods.  Students will learn to assemble the rods in trains to find the sum of two digit numbers and rearrange the train components to practice decomposing base ten components - collecting together all the ten rods followed by the ones, standard order.  This will illustrate the Commutative Rule.

Mini-lesson:  Present the base ten blocks and review their use as mathematics manipulatives.  Review that the ten rods are the same length as ten unit cubes pushed together.  Practice making 2-digit numbers for students to identify how many tens and how many ones to show a number.  The rods and cubes should always be shown in a linear manner, not side by side.  Students are connecting number and length so be consistent with demonstrations and displays of number.

The example below (with a corresponding image above) gives the written example of how students should be thinking about decomposing numbers.  This is a complex visual and not intended for 2^nd grade students to understand on its own or create.  It should be used by the instructor to ensure that the steps to the Commutative Rule are followed. Carefully walk through each step of this problem with students using their collection of base ten blocks.  Students will move the ten rods and unit cubes in this sequence to see how grouping tens together and ones together.  Demonstrate that the length remains the same as the ten rods and unit cubes are collected together to show 20 + 30 and 1 + 4.

21 + 34 = (20 + 1) + (30 + 4)

= 20 + (1 + (30 + 4)) = 20 + ((1 + 30) + 4) = 20 + ((30 + 1) + 4) = 20 + (30 + (1 + 4))

= (20 + 30) + (1 + 4) = 50 + 5 = 55

Students will practice this activity using the following problems:

16 + 43 = (10 + 6) + (40 + 3)

28 + 21 = (20 + 8) + (20 + 1)

35 + 42 = (30 + 5) + (40 + 2)

Students will work on problems that do not require regrouping, or making new tens. Once students are comfortable decomposing numbers and demonstrating that length connects to the sum, more challenging problems will be introduced.  Students should recognize that 10 unit cubes will become a new ten rod.  Use the same rule and process to decompose the numbers.

14 + 38 = (10 + 4) + (10 + 8)

27 + 36 = (20 + 7) + (30 + 6)

These more challenging examples should only be used if the students show great understanding and can explain their thinking.  The practice of making new tens is an additional component to solving the next level of problems.

Activity Three – Connecting Counting Number to Measurement

Objective:  Students will use correlate base ten blocks to the number line

Procedure:  After learning to combine rods and compare rods, students can begin to work with the number line.  They will connect the counting number to measurement on the number line, continuing to use the base ten blocks. By placing ten rods and unit cubes directly on the number line, students will see the number/length correlation. They will learn that numbers on the number line describe distance.  Number lines can be made to about 60 or 70 depending on desk/table top size that the students will be working on.  Sentence strips are made of sturdy card stock and are long enough to create number lines.

Mini-Lesson:  Show the number line which corresponds directly to the base ten blocks.  Unit cubes should be the unit length (from 0 to 1) and it would follow that 10 rods would be the distance 10 on the number line.  Demonstrate that 24 in base ten blocks, when placed on the number line is 20 for the 2 tens and 4 for the unit cubes, showing the distance on the number line as 24.  Demonstrate several examples.

Students will work in groups of 2-3 and practice comparing number on the number line to length.  The instructor will call out numbers and students will demonstrate understanding by placing rods and unit cubes on the line, 10’s first followed by ones.  The next steps of this activity combine the understanding from Activity Two, the Commutative Rule.  The instructor gives two 2-digit numbers for students to place on the number line. They students will then apply the Rule and show the sum of the two numbers.  The example problems in the previous activity will work with this activity as well.

Activity Four: School-wide Number Line

Objective: Students will connect length with number using the distance available in our school hallway

Procedure:  Students will take the hundreds chart apart by tens and place the sections of 10 end to end to demonstrate length to see how much longer 100 is that 10.  Students will repeat this same idea in the hallway of the school to show how much farther away 1000 is from 100 by creating a school-wide number line with the origin at our classroom.

Mini-lesson:  Using the 100-chart similar to the one below, show that for ease of use, we place our tens on top of each other so they are together up to 100.  Demonstrate with a larger version, that if we cut the “decades” apart, we can create a 100-number line instead.  Students will need to help by attaching one decade to the next with tape and holding the example as it grows longer.

Students will use their 100-chart to create a number line.  They can attach their pieces to lengths of adding tape that unrolls as they attach a new decade.  This “number line” can be rolled up and kept for future activities.

Additionally during this activity, a number line with the unit measure of 1” will begin in the hallway directly outside of the classroom and continue down the corridor ending at 1000.  The unit measure can be adjusted based on the length of the hallway and total distance available. 

The completed hallway number line will demonstrate the concept of number meaning a distance from the origin, in this case, our classroom.  This number line can become the tool for many activities.  Placing students in locations that are a distance of 10 apart, then a distance of 20, and so on up to a distance of 100; solving addition and subtraction problems; reinforcing place value and other ideas that students may generate.