Mathematics Number Sense Grade 8

Grade 8 In the Area of: Number Sense & Number Systems
1	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Develop, defend, extend understanding of reason for the impossible division by zero.	Write various problems illustrating division by zero. Ask students to solve, discuss. Generate rubric for group presentation.	Work with small group to develop presentation with appropriate models to explain why division by zero is impossible.	Class-generated rubric.	Research zero as concept, entity, explain its significance in mathematics.	- Math text. - Reference material.
Grade 8 In the Area of: Number Sense & Number Systems
2	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Select and use appropriate method for computing from mental arithmetic, paper and pencil, calculator and computer methods.	Share examples of various types of problems. Students identify most appropriate method for them.	Work in small groups to discuss appropriate strategies to use to solve sample problems given by teacher. Discuss ways to check solutions as well.	Problem solution strategies can be idiosyncratic to individual.	Solve and express as a single fraction in lowest terms 1 + 1 + 1 + ... + 1__ 1X2 2X3 3X4 9X10 Explain process.	Teacher-generated sample problems.
Grade 8 In the Area of: Number Sense & Number Systems
3	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Apply the properties and models of subtraction to integers.	Review subtraction as inverse of addition. Model with integers using two-colored counters.	At sunset (6 P.M.) temperature is 0û C. If temperature drops a single degree for every 1/2 hour, what temperature will it be at midnight? 3:00 AM?	Student writes rule for subtracting integers and explains rule to class.	Brainstorm applications of addition and subtraction to real life problems.	- Math text. - Focus on Pre-Algebra. - Manipulative Interlude Algebra. - The Write Tool to Teach Algebra. - Calculator.
Grade 8 In the Area of: Number Sense & Number Systems
4	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Multiply and divide negative numbers.	- Review multiplication and division properties. Model application with positive and negative numbers, inverses, etc. - Search for Patterns activity, AIMS.	Work with partner to devise rule to solve following problem: On five consecutive days, the low temperatures in a city were5û C, -6û C, -8û C, -1û C, and 3û C. What was the mean low temperature for these days?	Student writes and explains rule using examples.	- Create profit/loss problems involving multiplication/division of positive and negative numbers. Share. - Zounds! , p.102-03 - No Place Like Home activity.	- Graph paper. - Calculator. - Math text. - Manipulative Interlude Algebra. - The Write Tool to Teach Algebra. - AIMS, April, 1996. - Zounds!, pp. 102-103.
Grade 8 In the Area of: Number Sense & Number Systems
5	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Identify and use Multiplication Properties of zero and negative one.	Review Multiplication Properties of zero and 1. Compare/contrast with -1.	Transform geometric shapes by multiplying coordinates. X * -1; Discuss/compare to original.	Demonstrates by pattern and example that 0x = x0 = 0,and that -1 times any number gives its opposite.		- Graph paper. - Math text.
Grade 8 In the Area of: Number Sense & Number Systems
6	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Solve, extend problems involving integers, rational & real numbers.	Use Venn diagrams or graphic organizer to help students differentiate between integers, rational and real numbers.	- Identify/sort/classify numbers. - Solve problems with various numbers as specified by teacher.	Quiz.	Write an essay explaining why irrationals are important members of the number family.	Math text.
Grade 8 In the Area of: Number Sense & Number Systems
7	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Discuss, describe the following topics: perfect numbers, permutations, palindromes, factorials, triangular & square numbers, and Fibonacci numbers.	Set goals and parameters for group presentations. Generate rubric with class. Provide resources. Group students and assign topics.	Work in small groups to research, prepare class presentations with appropriate visuals to teach one of topics as assigned by teacher.	- Class-generated rubric. - Teacher-generated quiz integrating questions from all class presentations.	Research famous mathematicians. Prepare biography to share with class.	- Internet. - Math text. - Reference materials.
Grade 8 In the Area of: Number Sense & Number Systems
8	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Solve, apply percentage problems.	Demonstrate how to solve percent of change, discount and mark-up problems.	Work with partner to create story flyer with product pictures, description, price. Markdown price for 15% sale (or amount determined by teacher). Share flyer with class. Compare.	- Accurate markdowns. - Appealing visual display.	Choose a collectible object. Gather data and find the percent of change in its value of its life. Make an assessment of whether or not the collectible is a good investment. Explain.	- Math text. - Calculator. - Spreadsheet software.
Grade 8 In the Area of: Number Sense & Number Systems
9	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Give examples of the distance between two points on the coordinate plane.	- Start with number line to demonstrate process for calculating distance between 2 points. - Give increasingly more complex applications for students to discuss and describe.	Work independently to solve this problem: I work 5 days a week, 50 weeks a year for 5 years. The streets in this area form a grid of squares each 1/16 on a side. So my home must be fewer than 16 blocks from work. On graph paper, choose a point identified as work, choose another as home so that I would have a minimum of 5 difference routes to work.	Student explains clearly how to fine distance between two points on coordinate plane using various methods: counting, Pythagorean theorem, distance formula.	Research Coriole's force. Prepare visual to explain impact on aviation and flight plans. Relate to mathematical concepts.	- Encyclopedia. - Internet. - Math text. - Geometry software: Astro Algebra - Graph paper.
Grade 8 In the Area of: Number Sense & Number Systems
10	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Create models demonstrating operations with integers (such as number line, chips, etc.).	Model, "problem of week": Introduce on Monday. Solve later in week. Explain thought process used and provide model of some kind.	Model the following and other similar problems: A boy bought a bicycle for $80 and then sold it for $75. Later he bought it back for $85 and resold it for $100. How much did he make?	Student-generated examples.	Figure out how long it would take to say your name a million times. Make model to explain thinking.	- Calculator. - Math journals. - Internet "Problem of day" sites.
Grade 8 In the Area of: Number Sense & Number Systems
11	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Identify specific irrational numbers on the number line.	Explain the difference between rational, irrational numbers. Give examples of repeating and terminating decimals. Give students examples to sort.	- Identifies specified numbers as rational or irrational. - Draws number line and shows the square root of 2 and PI and others as specified by teacher.	Student explains clearly in writing the difference between rational and irrational numbers; give examples.	Find 2 different square roots that are irrational numbers, but whose product is a rational number.	- Math text. - Number lines.
Grade 8 In the Area of: Number Sense & Number Systems
12	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Factor expressions with a common factor.	- Models factoring expressions. - Uses Base Ten blocks to show value visually. - Review divisibility rules.	Factor expressions as directed by teacher.	Quiz.	Logic Puzzle: In the clues below each variable represents a different digit 0 - 9. Determine value of each variable. g + g + g = d j + e = j g2 = d b + g = d f - b = c a x c = a i/h = a(h>a) Explain process and reasoning.	- Math text. - Base Ten blocks.
Grade 8 In the Area of: Number Sense & Number Systems
13	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Develop and apply number theory concepts (primes, factors, multiples) in real world and mathematical problem situations.	Review concept of prime, factors, multiples and process of factorization.	Work with partner to solve the following problem: Members of the school marching band wanted to arrange themselves in exactly the same number of players in each row. They tried rows of 2, 3, 4, but there was always one player left over. What's the least number of members in the marching band? Explain your answer.	- Demonstrates facility with factoring. - Explains process used to solve problem.	Independently investigate following puzzle: The numbers 4, 12 and 24 are all factors of a number (n). List three other factors of n. Explain reasoning and process.	Math text.
Grade 8 In the Area of: Number Sense & Number Systems
14	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Estimate and compare rational numbers.	Shows students how to apply benchmarks 1/2 and 1 to obtain approximate value. Ex: 1/2 + 5/6 5/6 > 1/2 so answer will be between 1 and 1.5 on number line.	Arrange similar problems on a number line as assigned by teachers. Base Ten values are important benchmarks.		For each problem in learning, write range of estimates. Solution falls between what interval?	- Math text. - Number lines.