Second Look - Volume of a Rectangular Prism Thinking out of the Box . . . Problem Student explorations and mathematical generalizations of a classic pre-calculus and calculus problem "The box problem."

What Else Can You Do with an Open Box? Starting with the classic Open Box problem, we present extensions of this problem that can be used in high school mathematics classes. We also challenge high school teachers to use this process of problem analysis in their own practice as a way to enrich the content of their lessons and as a means of individualized professional development.

Sharing Teaching Ideas: Optimization: A Project in Mathematics and Communication The mathematics in the problem addresses many of the NCTM's Standards, as well as reform-calculus initiatives. The opportunity for meaningful communication about the mathematics is a vital component that was met well in the context of the assignment.

Illuminations Lesson: Popcorn Anyone? This lesson can be used for students to discover the [[#|relationship]] between dimension and volume. Students create two rectangular prisms and two cylinders to determine which holds more popcorn. Students then justify their observation by analyzing the formulas and identifying the dimension(s) with the largest impact on the volume.

A4

Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.

Demonstrate an understanding of factors of whole numbers by determining the:

prime factors

http://www.mrlsmath.com/mr-ls-videos/kenken-a-video-introduction-to-the-3x3-puzzle/ (KenKen Puzzles - Introductory Video) KenKen – Introduction and Strategy Tips to Solve a 4×4 Puzzle (KenKen Puzzles - Introductory Video) Daily KenKen® Puzzles Now on Illuminations! Rev up your grey cells every day with a KenKen puzzle! These mind [[#|exercises]] combine the logic of Sudoku with arithmetic operations. Now, thanks to an agreement with Nextoy LLC four new KenKen puzzles will be posted daily—that’s every day, Monday through Sunday—on the Illuminations site. The daily puzzles range from easy to difficult, with some involving only addition others using all four operations. You can solve the puzzles online or print them for your students. Solutions to each puzzle will be posted the next day. Be sure to stop back daily to check your answers and get four new puzzles!

Demonstrate an understanding of the multiplication of polynomial expressions (limited to monomials, binomials and trinomials), concretely, pictorially and symbolically.

Measurement | Algebra & Number | Relations & Functions | Relations & Functions Curriculum-Wide Resources | Curriculum-Wide Resources

## Table of Contents

## Measurement

## A1

Solve problems that involve linear measurement, using:## A2

Apply proportional reasoning to problems that involve conversions between SI and imperial units of measure.## A3

Solve problems, using SI and imperial units, that involve the surface area and volume of 3-D objects, including:## NCTM

Second Look - Volume of a Rectangular PrismThinking out of the Box . . . Problem

Student explorations and mathematical generalizations of a classic pre-calculus and calculus problem "The box problem."

What Else Can You Do with an Open Box?

Starting with the classic Open Box problem, we present extensions of this problem that can be used in high school mathematics classes. We also challenge high school teachers to use this process of problem analysis in their own practice as a way to enrich the content of their lessons and as a means of individualized professional development.

Sharing Teaching Ideas: Optimization: A Project in Mathematics and Communication

The mathematics in the problem addresses many of the NCTM's Standards, as well as reform-calculus initiatives. The opportunity for meaningful communication about the mathematics is a vital component that was met well in the context of the assignment.

Illuminations Lesson: Popcorn Anyone?

This lesson can be used for students to discover the

[[#|relationship]]between dimension and volume. Students create two rectangular prisms and two cylinders to determine which holds more popcorn. Students then justify their observation by analyzing the formulas and identifying the dimension(s) with the largest impact on the volume.## A4

Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.Pearson just posted their first mathematics app on iTunes. The trig app is free for download. Here is a direct link to where it sits via the iTunes app store:

http://itunes.apple.com/ca/app/trigonometry/id413309124?mt=8http://www.touchtrigonometry.org## Algebra & Number

## B1

Demonstrate an understanding of factors of whole numbers by determining the:http://www.mrlsmath.com/mr-ls-videos/kenken-a-video-introduction-to-the-3x3-puzzle/ (KenKen Puzzles - Introductory Video)

KenKen – Introduction and Strategy Tips to Solve a 4×4 Puzzle (KenKen Puzzles - Introductory Video)

Daily KenKen® Puzzles Now on Illuminations!Rev up your grey cells every day with a KenKen puzzle! These mind[[#|exercises]]combine the logic of Sudoku with arithmetic operations. Now, thanks to an agreement with Nextoy LLC four new KenKen puzzles will be posted daily—that’s every day, Monday through Sunday—on the Illuminations site. The daily puzzles range from easy to difficult, with some involving only addition others using all four operations. You can solve the puzzles online or print them for your students. Solutions to each puzzle will be posted the next day. Be sure to stop back daily to check your answers and get four new puzzles!- greatest common factor
- least common multiple
- square root

http://ronblond.com/M10/rootAP/index.html (Square Root Applet)## B2

Demonstrate an understanding of irrational numbers by:## B3

Demonstrate an understanding of powers with integral and rational exponents.## B4

Demonstrate an understanding of the multiplication of polynomial expressions (limited to monomials, binomials and trinomials), concretely, pictorially and symbolically.## B5

Demonstrate an understanding of common factors and trinomial factoring, concretely, pictorially and symbolically.## Relations & Functions

## C1

Interpret and explain the relationships among data, graphs and situations.## C2

Demonstrate an understanding of relations and functions.## C3

Demonstrate an understanding of slope with respect to:## C4

Describe and represent linear relations, using:## C5

Determine the characteristics of the graphs of linear relations, including the:## C6

Relate linear relations expressed in:y=mx+b)Ax+By+C= 0)y–y1 =m(x–x1)) to their graphs.## C7

Determine the equation of a linear relation, given:- a graph
- a point and the slope
- two points
- a point and the equation of a parallel or perpendicular line

to solve problems.## C8

Represent a linear function, using function notation.## C9

Solve problems that involve systems of linear equations in two variables, graphically and algebraically.## Relations & Functions Curriculum-Wide Resources

Barbie Bungee (NCTM Illuminations Activity)Ted Talks: In Six Minutes or Less

Terry Moore on "Why Is 'x' The Unknown?"

## Curriculum-Wide Resources

## LearnNowBC

## Mc-Graw Hill Ryerson Mathematics 10 Information Centre

## Open School BC

- http://order.openschool.bc.ca/Product/CourseDetail/k12g_7540006041

Note: The Open School BC resources are not free.## Saskatchewan Ministry of Education

https://www.edonline.sk.ca/webapps/moe-curriculum-BBLEARN/index.jsp?lang=enhttps://www.edonline.sk.ca/webapps/moe-curriculum-BBLEARN/index.jsp?lang=fr (Français)

Foundations of Mathematics and Pre-calculus 10 (2010)