Artifact 3.1 Solving Equations with Number Lines

Maria Sideri
Wheelock College
Lesson Plan

Grade Level: 2
Date: November 9, 2011
Time: 1:00-2:00pm
Subject Area: Mathematics-Number Sense, Equations, and Number Lines

Materials Used:
Number line examples (mini number lines in class, big number line on rug, and real-life examples)
Solving Equations with Number Line Jumping Worksheet
Bonus Worksheet (number line jumping with subtraction)
Chart Paper

Massachusetts Curriculum Frameworks for Mathematics:
Number Sense and Operations
Grades 1-2 Learning Standards

2.N.7 Demonstrate an understanding of various meanings of addition and subtraction,
e.g., addition as combination (plus, combined with, more); subtraction as comparison (how
much less, how much more), equalizing (how many more are needed to make these equal),
and separation (how much remaining).

Learning Goal:
To explore how to use and create number lines through solving addition equations.

Objectives:
Students will be able to recognize how a number line can be used (we will focus on the use of addition).
Students will be able to create their own number lines in order to help them add equation.

Prerequisite Knowledge:
Students need to have an idea of what a number line is (a sequence or order or numbers) in order to understand how to solve addition equations on a number line.

Assessment:
I will know that the students have reached the learning goal of this lesson when they can solve addition equations through the use of a number line and when they can create their own number lines in order to the solve addition equations on the worksheet and the equations they create.

Implementation:

1.Start off the lesson by asking the students what a number line is. Then on chart paper, write down their definitions as well as mine: “numbers standing on a line in order!” Then, go over examples of number lines they’ve seen in the classroom, or in everyday life. This will lead into the hook and hold-did you know that you can create your very own number lines!?...but first in order to create your very own number line, you have to figure out what it should be used for. (1:00-1:05)

2.Next ask the students how a number line can be used in mathematics. List these examples on chart paper. Explain to the students that in this lesson, we are focusing addition or (jumping on the number line). I will explain that in order to use addition, we will be solving equations! (1:05-1:10)

3.Next, on the long number line practice jumping with equations. I will have five examples and pick 5 students to come up on the rug and jump using the long number line and a close pin. We will use 1 digit number equations and 2 digit number equations for these examples. (1:10-1:15)

4.I will then go over with the students particular methods that the students used to jump (if they went one by one, by two, or by 5 or how they knew which number to start jumping with). Then, I will explain to them that when we complete a worksheet or solve equations, we won’t have a giant number line like this to use, or maybe the one we are provided with won’t have the numbers we need. This is how you can create your very own number line! (1:15-1:20)

5.Next, I will go over the worksheet with the students I created. The worksheet will include single digit as well as double digit equations. In order to solve these equations, I want to see a number line created for each of the equations. The key to making these number lines is that the number lines can start with the smallest number in the equation. We will do one example together as a class. (1:20-1:25)

6.Then, I will send the students back to their tables to complete the worksheet Solving Equations with Number Lines. If they finish early, they can complete the bonus worksheet using the number line for subtraction, and then go on to finishing their number scrolls or make-up work. (1:25-1:50)

7.At the end of the lesson, I will have the students come back together on the rug and we will discuss the worksheet, how number lines helped them to solve equations and some methods that they used to jump on the number line. (1:50-2:00)

Differentiated Instruction:
I believe that some students may struggle with creating a number line on their own based on the equation. Some may need to practice with a traditional number line starting from 0 and on. Therefore, I may provide such students with one to start to get used to adding on a number line, and then have them try starting at the lowest number in the equation and counting to the bigger number. Also, for students who finish quickly, I will provide a bonus worksheet that requires the students to show number lines using subtraction.

Reflection:
The students did very well with this lesson. At the beginning of the lesson, it was more difficult than I anticipated to explain to the students that a number line does not have to start at 0 or at 1. It took about 5 different examples to prove to the students that a number line can start with the biggest number in the equation. After practice altogether, the students started to understand. When it was time to work on the packet I created with different equations that needed to be solved using a number line, some students struggled starting the first line. Because I assigned one teacher or aid to each math table, this problem was solved fast and most of the students finished the packet about 10 minutes early. Therefore, we as a class had a longer discussion. This discussion went extremely well. I explained some patterns I saw that the students were using to step up their number lines, and most of the students explained that although the equations were simple to solve in their heads, it was difficult showing how they solved these problems through number lines. Therefore, the next day we practice more and went back over the areas that students found difficult or struggled with. Overall, the learning goal of this lesson was definitely met through their completion of the worksheets but also through their discussion of what the students were comfortable with, and what they found difficult.