In And Out Boxes

Math: In and Out Boxes Learning Objective: After learning about how to use a number line, the students will be able to infer and label the missing number on the number line by observing the surrounding numbers. The students will also apply their knowledge about number lines to identify the interval. Once students have identified a pattern on the number line, the students will identify and solve the patterns in an “In and Out” t-chart. CA Math Standards: Number Sense: 1.0 Students understand the place value of whole numbers: 1.1 Count, read, and write whole numbers to 10,000. 1.2 Compare and order whole numbers to 10,000. Mathematical Reasoning: 1.0 Students make decisions about how to approach problems: 1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. 1.2 Determine when and how to break a problem into simpler parts. 2.0 Students use strategies, skills, and concepts in finding solutions: 2.1 Use estimation to verify the reasonableness of calculated results. 2.2 Apply strategies and results from simpler problems to more complex problems. 2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning. Materials: 22 copies of number line Anticipatory Set: (15 minutes) 1. “Today we are going to be working on number lines. We can use number lines to help us order numbers. Sometimes we need to figure out a missing number on the number line though.” 2. “Let’s look at our worksheet that some number lines in it.” 3. “One of the first ways that we can find a missing number on the number line is to think about the half way mark. For example, if we’re going to be travelling from San Diego to San Francisco, we’re going to need to stopping points in order to make the drive more manageable. Number lines have stopping points as well. We will use these to make our “pit stops” and think about the interval.”

4. “For example, let’s look at these numbers: 1000, ___, 3000” 5. In this example, our missing number is 2000. If we were to skip count this,

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what number would we be skip counting by? 1000. What’s the next number after 3000? 4000. Write 1000 in each interval. Describe the interval as the distance between the two numbers like a pattern. Example 2: 30, 60, ____. 90. What is the difference between 60 and 30? 30. 60+30=90. What is the interval? 30. Example 3: 1420, _____, 1460. What is the difference between 1460 and 1420? 40. What is half of 40? 20. If we know that our interval is 20, then we can add 1420+20=1440. What number would come after 1460? 1480. Where would you place 1430? Now we’re going to estimate. Sometimes our number lines are not very exact. It is our job to try and make them as exact as possible. Example 4: 50 and 100. Let’s try to mark the number 68. In order to help us start, I think we should find the half way mark. 75. Now tell me when I should stop my finger. Slide finger along the number line. Mark were to estimate 68. Now lets try the number 88. Slide my finger and have the students tell me when to stop. Example 5: 0, ___, 1, ____, 2. Half of 1 is .5 or ½. The interval is ½. The missing numbers are .5 and 1.5.

Instruction: (5 minutes) 1. Remind students about our “In and Out machine.” We put 1 number in the machine and another number comes out of the machine. We need to figure out the pattern. Have students look at their in and out problem from yesterday.” Guided Practice: (15 minutes)

Out

#x2 In

1 2 3 5

2 4 6 12 20

Rule: #x2

Inverse rule: #/2

#+10 Out

In

15 4 9

25 14 48 104

Rule: #+10 Inverse Rule: #-10

In 1 5 10 8

Out 3 11 21 7

Rule: (#x2)+1 Inverse rule: (#-1)/2

In 3 6 11 30

Out 12 15 20 28

Rule: #+9 Inverse Rule: #-9

In 4 6 9 3

Out 12 18 27 30

Rule: #x3 Inverse rule: #/3

#+9

(#x2)+1 #x3

When students are working on this, have them pair share ideas. Independent Practice: (10 minutes) Number line Worksheet. 1. Students will identify the missing number on the worksheet. 2. Students will also identify the interval. Assessment: 1. The worksheets will be collected and graded. For students that struggled, we will do a review in a small group during math tomorrow. 2. Homework will be graded and recorded. Reflection: Were there points in the lesson that were not understood? Do I need to give additional help to the class or certain individuals?

Did I begin and end on time, check the classroom environment, and work through the mechanics of the class efficiently?

Did I set a pace that was neither too fast nor too slow?

What did I do particularly well today? What can I do better tomorrow?