Mathematics Patterns Relations and Functions Grade 6

Grade 6 In the Area of: Patterns, Relations, & Functions
1	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Graph, develop ordered pairs and relationships.	Encourage students to predict how changing a set of coordinates will affect the graph. Ask students to explain their thinking.	Plot a given set of points to create a picture. Students then generate a new set of points by applying some rule to the coordinates of the original picture. Ex: multiply each y coordinate by 2.	Students are presented with physical patterns and asked to express them algebraically.	Generate their own graph pictures, determine how they wish to enlarge, reduce, distort these pictures, then construct a rule and write clear directions for another student to complete the activity.	Algebra Thinking: First Experiences - Bob Wolcutt.
Grade 6 In the Area of: Patterns, Relations, & Functions
2	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Generate rules by simple concrete models.	Ask questions such as: " How many cubes would I need to construct the 3rd figure, 4th? 5th? 10th?100th? If I know the number of figures I want to make, how can I figure our how many cubes I will need?	MODELING ACTIVITY: with teacher direction, use cubes to build sets of items that follow a physical pattern. They make tables showing the number of cubes in each iteration of the figure, then look for numerical pattern that can be expressed using a variable.	Student should be able to accurately predict how a change in coordinates will affect the subsequent picture.	- Given a relationship expressed algebraically, build sets of models that fit the relationship. Students compare their sets for similarities and differences. - Use two types of pattern blocks in each model thus requiring the use of two variables in the algebraic expression.	Mathematics for the Middle Grades, NCTM 1982 Yearbook, pp. 102-117.
Grade 6 In the Area of: Patterns, Relations, & Functions
3	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Develop order of operation patterns and results on a calculator.	Supply students with a variety of calculators, some of which follow the order of operations automatically and some of which do not.	Attempt to solve a given set of problems on their calculator. When they discover that others in the class have different answers, discuss possible reasons. Once they have discovered order of operations to be the reason shy, students can determine which calculators use order of operations automatically and which do not.	Students write their own problems that will produce incorrect answers if the order of operations is not used.	Rewrite given problems to show the order in which items must be entered into the calculator to show how life was in the days when calculators could not follow the order of operations.	Order of Operations - Abigail Silver
Grade 6 In the Area of: Patterns, Relations, & Functions
4	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Identify, develop patterns in tables, graphs, rules, etc. to solve problems.	Show work for two or more patterns. Ask students to compare the rules and tables of each. Use those to explain similarities/differences in corresponding graphs.	For the MODELING ACTIVITY described above, graph their results and use their equations and graphs to predict new values. Students compare graphs of different patterns and begin to make predictions of how specific equations will look when graphed. Ex. x=y is a diagonal line intersect the origin. Another similar line is x=-y	Given two patterns, students identify the pattern that will generally require more cubes to construct and explain how the subsequent graphs will be similar or different.	Given a table, write a rule to show the pattern in the table, supply new numbers for the table and graph the points.	Algebra Thinking: First Experiences - Bob Wolcutt.
Grade 6 In the Area of: Patterns, Relations, & Functions
5	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Use variable to symbolize relationships between the four fundamental operations.	Point out equivalent expressions that are written differently such as a= I/2 b x=y/2. Challenge the class to find several ways of expressing each pattern.	In the MODELING ACTIVITY described on p. 178, students will find a variety of ways of expressing the same relationship. Ex: 2x +3 = x+x+ 3 .	Generate multiple ways to correctly express a given relationship algebraically.	Use manipulatives and drawings to write a journal entry showing why two expressions are equivalent.	Algebra Thinking: First Experiences - Bob Wolcutt.
Grade 6 In the Area of: Patterns, Relations, & Functions
6	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Solve, develop simple linear equations using manipulatives and models.	Encourage students to verify that their equation, table and graph are all consistent with each other. Help them use their physical models in making necessary changes.	In the MODELING ACTIVITY described on p. 178, students will write an equation showing the relationship between the iteration and the number of cubes needed in the model. They substitute numbers from their tables to check their equation.	- Given a physical pattern, students construct a table and express the relationship of paired items algebraically. - Given an algebraic equation, students construct a set of models to demonstrate the corresponding pattern.	Given a table, write an equation that describe the pattern in the table.	Algebra Thinking: First Experiences - Bob Wolcutt.
Grade 6 In the Area of: Patterns, Relations, & Functions
7	Outcome (The student will...)	Instructional Strategies (The teacher may...)	Learning Activities (The student may...)	Assessment	Extension (The student will...)	Resources
	Identify mathematical relationships occurring in other curricular areas (art, literature, etc.).	- Demonstrate the application/ integration of mathematical concepts through the reading of Gulliver's Travels by Swift. - Create a bulletin board area designated Math Applications.	Bring in examples of math concepts in other curricular areas to share with class and post on bulletin board.		Publish an original piece of fiction that incorporates math concepts and/or patterns. Share with an appropriate audience.	- Gulliver's Travels - Jonathan Swift. - Bulletin board.