Lesson plan
|Math Lesson: Computation with Rational Numbers |Grade Level: 7 |
|Lesson Summary: |
|The teacher reviews properties of whole numbers and the leads students through building a number line with positive and negative integers and rational numbers. |
|Students next use a number line to add and subtract rational numbers. Then students create examples of each property using rational numbers. Advanced students |
|investigate the term integer and compare it to rational number. Struggling students engage in creating examples of each property using integers. |
|Lesson Objectives:. |
|The students will know… |
|the differences between fractions, decimals, and positive and negative integers. |
|how to apply the properties of arithmetic to rational numbers. |
|The students will be able to… |
|add and subtract rational numbers using a number line. |
|identify the additive inverse of numbers. |
|use properties of arithmetic to calculate with fractions, decimals, and integers. |
|Learning Styles Targeted: |
| |
| |
|Visual |
| |
|Auditory |
| |
|Kinesthetic/Tactile |
| |
|Pre-Assessment: |
|Write the following equations on the board, and then ask students to explain the properties of addition or multiplication that each represents: |
|3 + 2 = 2 + 3 and 3 × 2 = 2 × 3 [Commutative property: the order in which two numbers are added or multiplied does not matter.] |
|(3 + 2) + 4 = 3 + (2 + 4) and (3 × 2) × 4 = 3 × (2× 4) [Associative property: When three or more numbers are added or multiplied, the answer is the same regardless|
|of the grouping of the factors.] |
|(12 ÷ 4) = (8 ÷ 4) + (4 ÷ 4) [Distributive property over addition: The factors in addition, subtraction, multiplication, and division can be decomposed and |
|operated on individually and then added together.] |
|3 – 2 = 1 and 2 + 1 = 3 and 6 ÷ 2 = 3 and 3 × 2 = 6 [Inverse operations of addition and subtraction and multiplication and division.] |
|3 × 1 = 3 and 3 ÷ 1 = 3 [Identity property of multiplication: Any number multiplied or divided by 1 is itself.] |
|3 + 0 = 0 and 3 – 0 = 3 [Zero property of addition and subtraction/Identity property of addition] |
|3 × 0 = 0 [Zero property of multiplication] |
|Note students who appear to have little awareness of the properties of arithmetic. |
|Whole-Class Instruction |
|Materials Needed: Number Line*, Properties of Operations* |
|Procedure: |
|Presentation |
|Draw a long horizontal number line on the board and put arrows on either end. Place a 0 in the middle of the number line and 5 on the positive end before the arrow|
|and -5 before the negative end arrow. |
|Have student volunteers place whole positive and negative integers 1 to 5 and –1 to –5 on the number line, spacing them as equally as possible. Applaud any efforts|
|to use a measure to make equal divisions between numbers. |
|Ask what comes halfway between 1 and 2. As students provide the answer, write [pic] above the number line and 1.5 below the number line. |
|Then ask what comes halfway between 1 and 1.5. As the answer is given, write [pic] above the number line and 1.25 below the number line. Then fill in the halves |
|and quarters between each positive integer on the number line. |
|Ask whether the opposites of these numbers would be the same distance from zero on a number line as the positive numbers, and once students agree that they would, |
|include the same negative rational numbers as positive rational numbers. |
|Write the words: positive integer, negative integer, and rational number on the board and discuss the definition of each as a whole number, a negative whole |
|number, or a number between two integers that can be expressed as a fraction, decimal, or ratio. |
|Using the number line, ask students to show you how to add 2 to 2.5 or [pic]. [By hopping to 3.5 then 4.5 while counting +1, +2.] |
|Using the number line, ask students to show you how to subtract 4 from [pic]. [By hopping to [pic], [pic], [pic], and then [pic] while counting -1, -2, -3, -4.] |
|Using the number line, have students tell you how to add 2.25 to -4.5. [First, add 2 to -4.5 by hopping to -3.5 then -2.5 while counting +1, +2. Then, add 0.25 to|
|-2.5 by hopping to -2.25 while counting +0.25.] |
|Have students explain why -3.5 + 4.25 = 0.75. |
| |
|Guided Practice |
|Distribute the Number Line to students. Have them plot 0 and then plot the positive and negative integers. |
|Next have them label positive and negative halves with fractions above the number line and decimals below. |
|Have them plot positive and negative 1/4s and 1/8s in decimals and fractions. |
|Now play a round of follow the leader by calling out a series of addition and subtraction equations and having students add and subtract to see if they can all |
|follow the sequence and end up on the same place on the number line. |
|Tell everyone to start at 2 and then follow this sequence +2, -1.5, +1, [pic], +[pic]. [Students should wind up at [pic].] Then repeat the sequence starting at the|
|additive inverse of 2, which is -2. [Students should wind up at [pic].] Explain the difference in the result by comparing the difference in the additive inverses. |
|Discuss why they might or might not have arrived at the same point on the number line. Continue with new sequences that you record on the board until all students |
|are able to follow the sequence. |
| |
|Independent Practice |
|Divide the class into pairs. Hand out the Properties with Operations worksheet, and have students create one example of each property using either decimals or |
|fractions. After ten minutes have students present their findings and discuss their reasoning. |
| |
|Closing Activity |
|Have students present and compare their examples of each property and confirm that the same properties used in calculating whole numbers are used when calculating |
|rational numbers. |
| |
|Advanced Learner |
|What Is an Integer? |
|Materials Needed: Internet access or dictionary |
|Procedure: |
|Have students investigate the etymology of the word integer and how it is used in mathematics. Have them compare the words integer and rational number to |
|distinguish between the two. |
|Have them present their findings to the class. |
|Struggling Learner |
|Properties of Whole Numbers |
|Materials Needed: Properties of Operations* master |
|Procedure: |
|Divide students into groups of two and give them the Properties of Operations. |
|Have each group create an example of each property using whole numbers. |
|Review and compare student results and have them explain their reasoning. |
*see supplemental resources
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