Adding with the Number Line

7/28/2019 Adding with the Number Line

1/4

2-1Adding with the Number Line 2-1

Abasic view of addition is one of joiningor counting on from an initialamount.This process is easily modeled with single blocks on numberlines. This approach works well for small numbers and helps to further

students understanding of addition and the development of mental

computation strategies.

Examples in this section all result in sums less than 100 in order to fit on

the labeled number lines. For work with larger numbers, use the 01000

number line or several unlabeled lines clipped together.The unlabeled linesare particularly appropriate for students who are ready for a challenge.

Joining Blocks on the Number Lines

To demonstrate, present a story problem such as theone that follows.

Keith has 38 blocks.

Shana has 17 blocks.

How many do they have when they put their blocks together?

Ask two volunteers to model the story problem withnumber lines. They will place 38 blocks on one lineand 17 on another line, and then combine the blockson one line. This can be done most easily by simplysliding the entire row of blocks from one line onto theend of the other line. Some students, however, mayprefer to count the blocks one by one.

After the volunteers have found the answer, ask,

What number sentence can you write to represent this situation?

When students have agreed to the sentence 38 + 17 =55, make sure they can relate the numbers and signs totheir actions with the blocks and to the story problem.

Students repeat this activity in small groups, placing 50or less blocks on two separate number lines and then sliding them together onone line to find the total number. Once familiar with the task, students shouldrecord their actions. Students will often use the wordsjoin and addas they

To combine 38 and 17 blocks on two numberlines, students slide them together on a single

line so they reach 55.

Focus Exploring the properties of addition and

developing mental computation skills


2/446

2-12-1describe their work, and some may write addition number sentences. Studentscan then tell their classmates what they did and share their recordings.

Exploring the Commutative Property

Present a card with the number 45 written on it and ask one student to showthat number of blocks on a number line. Give a second student a card withthe number 23, and have the student place that many blocks on another line.The second student then slides those blocks onto the first line and tells thenumber in all. Ask,

What number sentence can you write to represent this action?

To establish the connection between joining and separating blocks on the

line, ask the second student,If you took your blocks back to your line, how many would be left here?

Have the student remove the blocks and check. Then ask the first student,

If this time you take your blocks (pointing to line of 45) and put them on this line

(pointing to the line of 23), how many blocks will there be on the line? What

number sentence can you write to represent this action?

Again, have students place the blocks to check. Provide several more exam-ples. Encourage students to predict the outcome before they take back or join

the blocks and eventually to generalize that changing the order does notchange the sum (a + b = b + a).

Addition with More Than Two Addends

Present an example such as 23 + 16 + 45. Ask students how they might usenumber lines to find the total. The process is the same; they represent thethree numbers separately and then join them on one line. Have studentsexperiment with the order in which they join the numbers to further gener-

alize that regardless of the sequence, the sum is the same.

Reordering addends is a useful mental computation strategy. To encouragethis, have students find the solution to examples such as 27 + 14 + 53. Askthem to discuss which order for these addends works best for mental compu-tation, and why.


3/4

2-12-1 Predicting Totals

As students continue to represent addition examples and story problems onthe number line, encourage them to think about what the result will be

before they combine the two groups of blocks. Initially, students may usetheir hands to approximate the length of the second quantity and then thinkabout increasing the first amount by that length. Some students may note thenumber of longer hash marks (tens) in the second quantity, and count upfrom the first number by that amount. You might also provide a benchmark,asking questions such as,

Will there be more or less than 60 blocks when you put these two groups together? Why

do you think so?

Finally, ask students to predict exact outcomes before they combine the

blocks. Students can place markers on the line to show their predictedanswers. Begin with examples that do not require regrouping, such as 27 + 30and 26 + 32. Then challenge students with examples such as 67 + 28 and 16 +28 + 34. Invite students to explain how they arrived at their predictions.Students then place the blocks to check.

With more than two addends, encourage students to examine the order inwhich they add. Ask,

Do you get the same answer regardless of the order in which you add the numbers? Are

some orders easier than others? Why?

Through repeated opportunities to predict exact answers before actuallycombining or counting the blocks, students develop good number sense andmental computation skills. Such abilities take time to develop, but they arevery valuable in real-world situations. Encourage students to participate in theproblem-solving process of predicting answers correctly, and ask them toexplain their process for doing so.

Practicing Key Ideas

Together in a LineWrite numbers less than 25 on index cards, one number per card. Students work in

groups of two to four. Each student turns over a card and shows that number on a

separate number line. Students then combine the blocks on a single number line

and record the corresponding number sentence.

With more than two addends, students can take back their blocks and join them in

a different order. They can also identify which order they find easier and why.


4/448

Predict Exactly

Students play in teams of two players, each team having 50 blocks and a number

line. Each team places some of their blocks on a separate number line.Together, the

two teams decide on whose line to combine the blocks.Each team places a marker

on that line to show how many they think there will be when the blocks are com-bined.Together the students place the blocks to check.

Assessing Learning

1. Ask the student to show 57 on one number line and 36 on another line.Then say,

Show me how to combine these blocks and find the number in all. Then write a

number sentence to record your work.Does the student

read the total number from the line or recount the blocks? correctly identify the total? correctly write the corresponding number sentence?

2. Present the example 24 + 58 and ask the student to find the answer usingthe blocks and two number lines. Then ask the student to find 58 + 24and explain his or her thinking. Does the student model the process correctly? find the correct answer? immediately realize that the answer to the second example is the same,

or use the blocks to find the answer? clearly explain his or her thinking?

3. Have the student represent 46 + 28 on the number lines. Before havingthe blocks combined, ask,

If you place these blocks on the same line, where do you think they will end? Why do

you think so?Have the student combine the blocks to check. Repeat with a differentexample, this time using the unlabeled side of the line. Does the student predict correctly? do so on a labeled and unlabeled number line? clearly explain his or her thinking?

4. Present a story problem. For example:

At the field day, 29 boys and 38 girls entered the sack race.

How many children entered the sack race?Does the student use the blocks and number line to find the answer? answer correctly?

2-12-1

Documents

Adding with the Number Line