Pre-calculus 11 Pacing Guide - This pacing guide replaces the previous yearly plan. It has been updated to reflect removed outcomes and provide flexibility for responsive instruction.
Pre-calculus 11 Desmos Activity Collection - A collection of online student Desmos activities organized by unit.
AN03 - It is intended that the equations will have no more than two radicals.
AN02 Students will be expected to solve problems that involve operations on radicals and radical expressions with numerical and variable radicands.
AN02.01 Compare and order radical expressions with numerical radicands in a given set.
AN02.02 Express an entire radical with a numerical radicand as a mixed radical.
AN02.03 Express a mixed radical with a numerical radicand as an entire radical.
AN02.04 Perform one or more operations to simplify radical expressions with numerical or variable radicands.
AN02.05 Rationalize the denominator of a radical expression with monomial or binomial denominators.
AN02.06 Describe the relationship between rationalizing a binomial denominator of a rational expression and the product of the factors of a difference of squares expression.
AN02.07 Explain, using examples, that (–x)² = x² , √ (x²) = |x| , and √ (x²) ≠ ± x.
AN02.08 Identify the values of the variable for which a given radical expression is defined.
AN02.09 Solve a problem that involves radical expressions.
AN03 Students will be expected to solve problems that involve radical equations (limited to square roots).
(It is intended that the equations will have no more than two radicals.)
AN03.01 Determine any restrictions on values for the variable in a radical equation.
AN03.02 Determine the roots of a radical equation algebraically, and explain the process used to solve the equation.
AN03.03 Verify, by substitution, that the values determined in solving a radical equation algebraically are roots of the equation.
AN03.04 Explain why some roots determined in solving a radical equation algebraically are extraneous.
AN03.05 Solve problems by modelling a situation using a radical equation.
Additional Resources and Activities for AN02 (radical expressions):
Which One Doesn't Belong? Radicals - A discussion prompt to remind students of radical terminology and rational/irrational numbers.
Same and Different - Ask student to compare and contrast a radical expression and a polynomial expression. How are they similar or different? How are the rules for simplifying polynomials and radials alike or different?
Radical Operations Row Game - A row game worksheet has two columns. A pair of students work together to evaluated the radical expressions on the sheet. Student A answers the questions in Column A. Student B answers the questions in Column B. The problems in each row are different but have the same solution. If the students don't get the same solution, they work together to figure out where the error is. Immediate feedback and students helping students.
The Sturdy Rectangle SSDD Problem - A set of four related problems involving radicals. A great warm-up problem. This problem and more can be found on the SSDD problems website.
Irrational Number Spiders - Math "spiders" are a nice math routine to project on the LCD or to print off as a worksheet.
Radical Pyramid - Place bricks in the pyramid shape so that each brick is the sum of the two brisk beneath it.
Radical Expressions Scavenger Hunt - Students work in small groups to solve a series of questions. The solution to each question will lead to a new problem. Once students find their way back to their starting problem, they have completed the loop. Students can record their work on a separate sheet. You could also do this activity as a "question stack" with small groups working together at their desks. A question stack explanation card is a useful resource when doing this.
The Root of the Problem - Investigate the sum of a complicated looking expression with 100 terms with radicals. You don't need to know about series to solve this one.
Multiplication Squares - These puzzle like questions let students practice radical multiplication. These are very similar to a Yohaku puzzle.
Increasingly Difficult Questions (Surds) - These questions increase the difficulty of questions at an increased rate as students work through an exercise.
Pedantic Arithmetic Rules - Some food for thought... "There is a old taboo against having radicals in the denominator of a fraction. For example, 3/√5 is not allowed and should be rewritten as 3√5/5. This is an arbitrary convention now, though there once was a practical reason for it, namely that in hand calculations it’s easier to multiply by a long decimal number than to divide by it. So, for example, if you had to reduce 3/√5 to a decimal in the old days, you’d look up √5 in a table to find it equals 2.2360679775. It would be easier to compute 0.6*2.2360679775 by hand than to compute 3/2.2360679775." (see the bottom of page 274 in the Pre-Calculus 11 textbook for Radicals in Simplest Form)
Additional Resources and Activities for AN03 (solving radical equations):
Radical Equations Open Middle problem - Using the digits 0-9 at most one time each, make both of these equations true.
Who Wins the Race - Alice and Briana each participate in a 5-kilometer race. Each of their progress is modeled by an expression. Who wins the race?
Radical Equations Row Game - A row game worksheet has two columns. A pair of students work together to solve the problems on the sheet. Student A answers the questions in Column A. Student B answers the questions in Column B. The problems in each row are different but have the same solution. If the students don't get the same solution, they work together to figure out where the error is. Immediate feedback and students helping students.