In this seminar, you will engage in hands-on activities and authentic assessment tasks, using proven instructional strategies and games that foster deep understanding leading to student success in algebra. Each activity is tied to specific Common Core State Standards for Mathematical Content and Mathematical Practice. Connections are made to arithmetic number concepts to illustrate that algebra is really “generalized arithmetic.” Real-world applications — including the use of algebra to justify number “tricks” — are used to motivate students and illustrate why algebra is important.
You will leave the seminar with a wealth of material and ideas designed to support instruction of both regular and special-needs students.
TOPICS AND REPRESENATIVE COMMON CORE STATE STANDARDS
- Pre-Algebra Warm-ups and Sponge Activities
Experience how using such activities helps students revisit important skills throughout the year.
- The Common Core State Standards that Lead to Success in Algebra
Examine “Progress to Algebra in Grades K–8,” a document outlining the CCSS “clusters” in Grades K–8 that lead to
progress in Algebra from the “Publishers’ Criteria for the Common Core State Standards for Math.”
- What Is Algebra? What Is a Variable?
Examine four different ways variables are used (6.EE.5. MP2: Reason abstractly and quantitatively.)
- What Does the Equal Sign Mean? Instructional Game: Balance the Number Sentence!
This game promotes the meaning of the equal sign, using mental math and trial-and-error thinking to balance open
number sentences involving addition, subtraction, multiplication, and division. Play with whole numbers or fractions.
(4.NBT.6, 5.NF.4, 5.NF.7, 6.NS.1, 6.EE.5. MP2: Reason abstractly and quantitatively. MP6: Attend to precision.)
- Understanding and Evaluating Numerical and Algebraic Expressions
- a. Reading Mathematics with Precision; Expression Match
Match verbal and visual representations with algebraic expressions. (6.EE.1, 6.EE.2a. MP4: Model with Mathematics.
MP6: Attend to precision.)
- b. Introducing Algebra Egg-spressions
Use plastic eggs with hidden numbers as a way to introduce how to write and evaluate algebraic expressions. Plan
for egg-citement! (5.OA.1, 5.OA.2, 6.EE.2, 6.EE.6. MP4: Model with mathematics. MP7: Look for and make use of structure.)
- c. Applying Laws of Arithmetic to Evaluate Algebraic Expressions: Bridging Arithmetic and Algebra
Use patterns from evaluating numerical expressions to help you evaluate algebraic expressions. (6.EE.1, 6.EE.2, 6.EE.3,
6.EE.6. MP2: Reason abstractly & quantitatively. MP7: Make use of structure. MP8: Express regularity in repeated reasoning.)
- Bridging Arithmetic and Algebra with the Distributive Property
Explore how understanding the Distributive Property promotes success with algebra. (3.OA.5, 3.MD.7c, 4.NBT.5, 6.NS.4,
6.EE.3, 7.NS.2a. MP7: Look for and make use of structure. MP8: Express regularity in repeated reasoning.)
- Guess My Number!; Algebraic Card “Trick”
Use manipulatives, operations with variables, and algebraic reasoning to make generalizations as to why a “trick” works. (5.OA.1, 5.OA.2, 6.EE.2, 6.EE.3, 6.EE.6. MP4: Model with mathematics. MP7: Look for and make use of structure.)
- More Guess My Number! “Tricks” — It’s Not Magic; It’s ALGEBRA!
Make connections among verbal descriptions for a “trick,” numerical examples (arithmetic), and algebraic expressions.
Conclude that repeated numerical examples do not prove a trick works—but ALGEBRA does! (5.OA.1, 5.OA.2,
6.EE.2, 6.EE.3, 6.EE.6. MP2: Reason abstractly and quantitatively. MP3: Construct viable arguments. MP7: Make use of structure.)
- Strategies to Teach Operations with Integers
Use models – 2-color tiles, gains/losses on a football field, and future/past financial transactions — and algebraic
reasoning — to discover rules for integer operations. Explore why the product of two negative numbers is positive.
(6.NS.5, 7.NS.1, 7.NS.2, 7.NS.3. MP3: Construct viable arguments and critique reasoning of others. MP4: Model with mathematics.
MP7: Look for and make use of structure. MP8: Express regularity in repeated reasoning.)
- How Do Equations and Expressions Differ? Solving Equations and Inequalities
- a. A Balanced Approach to Solve Human Equations; Using Beans, Cups, & Toothpicks to Solve Equations (6.EE.4, 6.EE.5, 6.EE.6, 7.EE.1, 8.EE.7a. MP2: Reason abstractly and quantitatively. MP3: Construct viable arguments and critique
the reasoning of others. MP4: Model with mathematics.)
- b. Inequalities in the Real World; Operations with Inequalities (6.NS.7, 6.EE.5, 6.EE.8, 7.EE.1, 7.EE.4b. MP1: Make
sense of problems and persevere in solving them. MP4: Model with mathematics.)
- Using Bar Diagrams to Solve Algebra and Ratio / Proportion Problems
Use “Singapore-type” bar models to bridge “words to equations” to solve word problems. (6.RP.1, 6.EE.6 6.EE.7, 7.RP.2,
7.EE.1, 8.EE.5. MP1: Make sense of problems and persevere in solving them. MP4: Model with Mathematics.)
- Instructional Game: Getting Coordinated with “Battleship”
Explore ordered pairs in all four quadrants. Develop strategic mathematical clues to determine a ship’s location.
(5.OA.3, 5.G.1, 6.NS.6b. MP2: Reason abstractly and quantitatively. MP4: Model with mathematics.)
- Authentic Assessment: What Is It? How May It Be Used to Promote Algebraic Reasoning?
Explore authentic (performance) tasks related to linear graphs and other topics to observe how the tasks allow students
to provide direct evidence of strong understanding. (8.F.2. MP3: Construct viable arguments. MP7: Make use of structure.)
- Mathematical Recreation: Solving Pre-Algebra Problems from NCTM’s “Cartoon Corner”
Activities: Easy as Pi? Infinitely NOT! Find x. Let’s Be Rational about Numbers. Is a Double Negative a No-No?
- How to Use Algebra to Have the Last Word on Almost Anything
One final “trick” to take back to your class. (7.EE.4, A.SSE.3. MP2: Reason abstractly and quantitatively.)
All teachers, including those teaching developmental curricula or math education teachers, should benefit from this
David B. Spangler
Recipient of the 2014 ICTM
Lee Yunker Mathematics
(Illinois Council of Teachers of Mathematics)
During the past 40+ years, David has
taught at the middle school, community
college, and university levels. He
currently teaches mathematics
methods courses for National-Louis
University, and he is a developer of
mathematics curriculum materials for
David has authored a number of math books for teachers and students, including Math for Real Kids, and Strategies for Teaching Fractions. He is co-editor of NCTM’s Cartoon Corner in Mathematics Teaching in the Middle School.