Get Your Junior High Math Program Rolling Webinar with Cathy Campbell Are you a new teacher, new to teaching math or have you changed the grade you are teaching? Join our webinar to learn more about the revised math Program of Studies. We will begin by looking at the resources you need to get started. We'll briefly look at how content has shifted across the grades, but more importantly we'll discuss the implications of the philosophy shift in 7-9 math classrooms. We will focus on personal strategies and problem solving. Digital resources and activities that support teaching mathematics will be shared as well. Follow up webinar on "Making Meaning in Junior High Math", on February 3, 2011.

Welcome! Where do you work? A. Edmonton B. Greater Edmonton area C. Somewhere else in Alberta D. Outside of Alberta

Place an icon in the area that best describes your experience teaching junior high mathematics. Never 1-3 years 4-9 years 10+ years

Place an icon below the picture that best describes your experience teaching math with the revised Program of Studies.

Place an icon below the grade(s) you teach: Grade 7Grade 8Grade 9

Resources Program of Studies Major Shifts Problem Solving & Personal Strategies

Resources

Program of Studies Intent Mathematical Processes Nature of Mathematics General Outcomes Specific Outcomes

Have you already purchased your resources?

Place an icon by the series that you use at your school.

Changes to the Alberta Program of Studies Western and Northern Canadian Protocol (WNCP) Common Curriculum Framework (CCF) Provinces Made Slight Changes Publishers

This document identifies these changes and in so doing identifies the differences between the WNCP CCF and the Alberta Mathematics K-9 Program of Studies.

Grade 8

Manipulatives Put icons by the manipulatives you use.

What other manipulatives do you use? Type in your answers on this page.

Is there anything else you can think of that you need to teach junior high math?

Program of Studies

Background Introduction Conceptual Framework for K-9 Mathematics Instructional Focus FRONT MATTER Pages 1 -15

Consider the following when planning for instruction: Integration of the mathematical processes within each strand is expected. INSTRUCTIONAL FOCUS Page 15

Consider the following when planning for instruction: Integration of the mathematical processes within each strand is expected. By decreasing emphasis on rote calculation, drill and practice, and the size of numbers used in paper and pencil calculations, more time is available for concept development. INSTRUCTIONAL FOCUS Page 15

Consider the following when planning for instruction: Integration of the mathematical processes within each strand is expected. By decreasing emphasis on rote calculation, drill and practice, and the size of numbers used in paper and pencil calculations, more time is available for concept development. Problem solving, reasoning and connections are vital to increasing mathematical fluency and must be integrated throughout the program. INSTRUCTIONAL FOCUS Page 15

Consider the following when planning for instruction: Integration of the mathematical processes within each strand is expected. By decreasing emphasis on rote calculation, drill and practice, and the size of numbers used in paper and pencil calculations, more time is available for concept development. Problem solving, reasoning and connections are vital to increasing mathematical fluency and must be integrated throughout the program. There is to be a balance among mental mathematics and estimation, paper and pencil exercises, and the use of technology, including calculators and computers. Concepts should be introduced using manipulatives and be developed concretely, pictorially and symbolically. INSTRUCTIONAL FOCUS Page 15

Consider the following when planning for instruction: Integration of the mathematical processes within each strand is expected. By decreasing emphasis on rote calculation, drill and practice, and the size of numbers used in paper and pencil calculations, more time is available for concept development. Problem solving, reasoning and connections are vital to increasing mathematical fluency and must be integrated throughout the program. There is to be a balance among mental mathematics and estimation, paper and pencil exercises, and the use of technology, including calculators and computers. Concepts should be introduced using manipulatives and be developed concretely, pictorially and symbolically. Students bring a diversity of learning styles and cultural backgrounds to the classroom. They will be at varying developmental stages. INSTRUCTIONAL FOCUS Page 15

What is essentially the same between the 1996 and 2007 Program of Studies?

Beliefs about Students Mathematical understanding is fostered when students build on their own experiences and prior knowledge.

Goal for Students Prepare students to use mathematics confidently to solve problems.

Teaching through Problem Solving Learning through problem solving should be the focus of mathematics at all grades.

Mathematical Processes The mathematical processes are intended to permeate teaching and learning.

Do you know the 7 process skills and where you can find them?

Major Shifts

Front matter Achievement Indicators vs. Illustrative Examples General Outcomes across the grades Wording of outcomes: “demonstrate an understanding of” Changes you may have already noticed in the Program of Studies

Gr 7 - adding & subtracting fractions and integers Gr 8 - multiplying & dividing fractions and integers Gr 8 - Congruence of polygons Gr 9 - Similarity of all shapes Gr 9 - Trigonometry and factoring polynomials has moved to high school Gr 9 - Circle properties added Some Content Changes Have you noticed any other differences?

“Demonstrate an Understanding of...” Grade 7: 8/25 ≈32% Grade 8: 6/17 ≈35% Grade 9: 7/22 ≈32%

6. Determine measures of central tendency for a set of data:  mode  median  mean. [PS] 1996

Demonstrate an understanding of central tendency and range by:  determining the measures of central tendency (mean, median, mode) and range  determining the most appropriate measures of central tendency to report findings. [C PS R T]

Changing Focus Conceptual Understanding Personal strategies Algebraic Reasoning Number Sense

More depth, less breadth Relationships among important mathematical ideas Why certain procedures work Conceptual Understanding Conceptual Understanding

More depth, less breadth Relationships among important mathematical ideas Why certain procedures work Conceptual Understanding

a) b) c)

More depth, less breadth Relationships among important mathematical ideas Why certain procedures work Conceptual Understanding

= 3 groups of 4 = 3 x 4 = 12 x + x + x + x = 4 groups of x = 4x

More depth, less breadth Relationships among important mathematical ideas Why certain procedures work Conceptual Understanding

Calculate this answer.

Did you solve it something like this?

04

03214

03214

03214

Concretely, pictorially & then symbolically =

Here’s another example: Concretely, pictorially & then symbolically

Here’s another example: Concretely, pictorially & then symbolically

Here’s another example: Concretely, pictorially & then symbolically

Here’s another example: Concretely, pictorially & then symbolically (2x 2 + 3x + 5) +(x 2 + 2x + 6) =3x 2 + 5x + 11

Personal strategies Students are encouraged to solve problems, complete computations and represent their learning in a way that is meaningful to them.

Personal strategies Students are encouraged to solve problems, complete computations and represent their learning in a way that is meaningful to them. Students are expected to be able to explain the personal strategies.

Personal strategies Students are encouraged to solve problems, complete computations and represent their learning in a way that is meaningful to them. Students are expected to be able to explain the personal strategies. Personal strategies must be accurate.

Personal strategies Students are encouraged to solve problems, complete computations and represent their learning in a way that is meaningful to them. Students are expected to be able to explain the personal strategies. Personal strategies must be accurate. Personal strategies become more efficient over time.

How many cookies?

Which fraction is larger? How do you know?

Which strategy did you use?

Common denominators of fifteenths? Draw pictures? Use a benchmark? Something different?

Algebraic Reasoning

8 + 4 = x + 5 For grade 8 students, what were some common answers to this question? Write your answers below.

10 grams

3 + 2 = 5 Grade 1: Concept of equality and record using equal symbol

Grade 2: Concept of not equal and record using not equal symbol ≠ 5

3 = 2 + Grades 3 and 4: Solve one-step equations using a symbol

Grade 5: Equations using letter variables 3 = 2 + n

6 = n = n + 2 Grade 6: Preservation of Equality

8 = 2n + 2 Grades 7 to 9: Algebraic Manipulation

How Many Blocks are in the bag?

Solve this equation using cubes. 2x + 8 = 16

Number Sense

BIG IDEA The place value system we use is built on patterns to make our work with numbers more efficient.

Create a number where you would say each of the following words: (Write it symbolically) TASK

million five sixty hundred thousand three four

million, five, sixty, hundred thousand, three, four Write your answers below.

Are these possible solutions? Why or why not? b) d) c) a) million, five, sixty, hundred thousand, three, four

FOLLOW-UP QUESTIONS How did you know your number would have at least 7 digits? million, five, sixty, hundred thousand, three, four

FOLLOW-UP QUESTIONS How did you know the digit 6 would be the middle digit in a period? million, five, sixty, hundred thousand, three, four

FOLLOW-UP QUESTIONS How did you know the digit 4 could be the right-hand digit in a period? million, five, sixty, hundred thousand, three, four

FOLLOW-UP QUESTIONS Could you have the digits 000 in the thousand period? million, five, sixty, hundred thousand, three, four

SUMMARY: Changing Focus ·Conceptual Understanding ·Personal strategies ·Algebraic Reasoning ·Number Sense

Teaching Through Problem Solving (and Encouraging Personal Strategies )

Program of Studies (page 8) A problem-solving activity must ask students to determine a way to get from what is known to what is sought.

Program of Studies (page 8) A problem-solving activity must ask students to determine a way to get from what is known to what is sought. If students have already been given ways to solve the problem, it is not a problem, but practice.

Program of Studies (page 8) A problem-solving activity must ask students to determine a way to get from what is known to what is sought. If students have already been given ways to solve the problem, it is not a problem, but practice. A true problem requires students to use prior learnings in new ways and contexts.

Program of Studies (page 8) A problem-solving activity must ask students to determine a way to get from what is known to what is sought. If students have already been given ways to solve the problem, it is not a problem, but practice. A true problem requires students to use prior learnings in new ways and contexts. Problem solving requires and builds depth of conceptual understanding and student engagement.

I will share a couple more examples here, but I will be presenting a follow-up webinar on Thursday, February 3, 2011, where we’ll spend more time on problem solving and personal strategies

OPEN QUESTION - NUMBER BIG IDEA: Number benchmarks are useful for relating numbers and estimating amounts.

Choose a number for the second mark on the number line. Mark a third point on the line. Tell what number name it should have and why. 0

000

000

What modifications could you make to this activity? 0

PARALLEL TASK - GEOMETRY BIG IDEA: Shapes of different dimensions and their properties can be described mathematically.

These two dots have the corner of a given shape.

Option 1: Make a square with these corners

These two dots have the corner of a given shape. Option 1: Make a square with these corners Option 2: Make a parallelogram with these corners

These two dots have the corner of a given shape. Option 1: Make a square with these corners Option 2: Make a parallelogram with these corners Option 3: Make an isosceles triangle with these corners

No matter which task was selected, students could be asked:

a)Describe your shape.

No matter which task was selected, students could be asked: a) Describe your shape. b) What name would you give your shape?

No matter which task was selected, students could be asked: a) Describe your shape. b) What name would you give your shape? c) How do you know it is the shape you say it is?

What modifications could you make to this activity?

Thank you! Cathy Campbell Consulting Services, EPSB