#MTBoSBlaugust Algebra 2 Curriculum Overview

For the past few years our Algebra 2 curriculum has been focused on functions.  First we explore them graphically, then we apply them in problem solving.  Each year we tweak the sequence just a bit.  But here is a general overview of suggested units by months (not exact months).

August: Introduction to Functions

• 8 functions:  linear, absolute value, quadratic, cubic, square root, exponential, logarithmic, rational
• Function notation
• Transformations
• Domain/Range

September:  Systems of Equations

• Linear Systems, Nonlinear Systems, 3 variable systems
• Solving by Graphing, Substitution, Elimination, Gaussian, Matrices
• Linear Inequalities and Optimization Problems
• Application Problems

October:  Quadratic Functions

• Attributes of the Quadratic Function, Analysis of the Graph
• Transformations
• Introduction of parabola as a conic section (conics taught in PreCalc)
• Forms of the equation: standard form, vertex form, transformation form, conics form
• Writing the equation that fits given criteria
• Solving Quadratics: factoring, roots, completing the square, formula
• Complex Numbers
• Application Problems

November:  Cubic Functions

• Attributes of the Cubic Function, Analysis of the Graph
• Transformations
• Factoring cubic patterns
• Solving by graphing or factoring

December: Polynomials

• Basic Operations including long division, synthetic division
• Factoring 
• Polynomial Theorems - roots, factors, 
• Key attributes of graphs - end behavior, number of roots
• Regression Equations - best fit polynomial models

January: Rational Functions

• Key attributes and analysis of graph
• Transformations
• Holes, Asymptotes (not slant - precalc)
• Basic Operations with Rational Expressions
• Simplify Complex Fractions
• Solve Rational Equations
• Application Problems

February: Concept of Inverse Functions and Radical Functions

• Inverse Functions
• Solving Problems using inverses
• Key Attributes of the square root and cube root functions
• Transformations
• Rational Exponents
• Solving radical equations
• Application Problems

March:  Exponential & Logarithmic Functions

• Attributes of exponential and log graphs
• Transformations
• Analysis of exponential function (growth vs decay)
• Writing an exponential function in recursive form
• Log Properties
• Finding the inverse 
• Solving equations
• Application Problems
• Analyzing Linear, Quadratic or Exponential

April:  Absolute Value Functions

• Introduction to Piecewise Functions
• Key attributes of the graph
• Transformations
• Solving equations and inequalities
• Application Problems

May:  Other Topics ... select as needed

• Wrap up previous topics  (most likely scenario)
• Review functions - finding commonalities and differences
• Introduce Sequences/Series (taught in PreCalc)

Fraction Stations - Understanding Concepts

Students need to have a deep understanding of fraction concepts.  Our textbooks often focus on the basic skills.  It’s important to provide opportunities for mathematical discourse, reason abstractly, and construct viable arguments.  I adapted problems from various sources to create five stations providing opportunities for elementary students to explain their thinking about the concept of a fraction, the meaning of fractions, and reason about equivalence and addition.

The stations address these Common Core State Standards:

•       CCSS.Math.Content.3.NF.A.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.

•       CCSS.Math.Content.3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

•       CCSS.Math.Content.4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

•       CCSS.Math.Content.4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

You can use the stations as journal entries, group work, formative assessment and purposeful practice.

Check out the stations here in my Google docs or here at my TpT store!

Let me know if the stations work well for you!

How do you challenge students to think deeply about fractions?

Primary Math Number Mysteries

Do you love a good mystery?

I am less than 100.I am an odd number.
My tens digit is the same as the number of days in a week.
My ones digit is the number of fingers on one hand.

What number am I?

Our math resources sometimes lack enough practice for students to build independent math skills. 

Number Mysteries is a free resource with eight place value mysteries that could be used as extra practice for seat work or a math center.

Download the pdf here or here!

In Number Mysteries, students identify a 2-digit number using clues. Clues involve common numbers such as “half of a dozen” or the “value of a nickel.”

Students could be asked to represent the mystery number using concrete materials, drawings, or in standard form.

After working through these exercises, students should create their own puzzles.  Student-created puzzles with illustrations could be put together in puzzle books and/or hung in math centers to challenge classmates.

Finished ... and the countdown begins!

WHEW!  We just finished our last lesson of required content this year!  It's been tough ... there have been times when we pushed on before students were ready.  But now we can say we faithfully taught all the required content before the high-stakes math test.  (The test counts 15% of the semester grade and a passing score is required for graduation  Our high schoolers have to pass 15 of these tests to graduate ... unless lawmakers make needed changes!)  Our big test is Monday, May 6.

We have 5 class days (actually 9 ... but we have A/B days) to go on a whirlwind review of key topics from this year.  Our PLC members each took a day and created 3 stations and/or activities for each of those days.  Our schedule looks like this:

Day 1: Foundation of Functions and Equations

• Interpret Data
• Solve Equations
• Solve Word Problems (in one variable)

Day 2:  Linear Functions

• Slopes and Intercepts
• Solving for "y"
• Converting to standard form

Day 3:  Linear Functions cont

• Writing/Graphing Equations
• Using Point & Slope
• Interpreting Equations/Graphs

Day 4:  Linear Functions cont

• Transformations
• Is it linear, quadratic or exponential
• Solving systems by graphing

Day 5:  Systems and Test-Taking Tips

• Solving systems using substitution/elimination
• Error Analysis in test taking
• Sharing test taking tips

Obviously there are some topics not included ... polynomials, laws of exponents, quadratics.  We focused on topics from first semester and on topics our students struggled with.

I'll share an activity or two soon ... but since I didn't create all the activities I need to check to see if my colleagues mind if I share them online.

How do you help students prepare for high-stakes testing?