Applications to download for today (list sent by June 23--free and for ipad unless noted):

Transcription

1 Applications to download for today (list sent by June 23--free and for ipad unless noted): Algebra Equation Builder Algebra Equation Balancer Algebra Card Clutter Algebra Tiles Action Grapher Cover Up (solving algebraic expressions) Diamond Factor Function Mystery Machine Hop the Number Line Inequality Kickoff Lion Grapher Linear Model Math Flyer ($0.99)/ Point Plotter Slope Slider (free/basic version of Math Flyer--iPhone and ipad) Submariner Algebra Tortoise and the Hare Algebra

2 Virtual Manipulatives for Teaching Algebra with ipads Dr. Mike Charles Dr. Linda Samek Pacific University Oregon Dr. Rachel Harrington Dr. Steve Rhine

3 Overview Algebra is the gateway to college & careers Alarming failure statistics 800 research studies on why reviewed by a statewide coalition of educators Emerging technologies could be part of the solution One ipad vs. class set

4 Virtual Manipulatives Addressing Student misconceptions in Algebra--there s an app for that... interactive visual representation dynamic construct math knowledge simple, focused on one concept

5 Task levels for apps Doing+Mathema)cs+ Genera/ve' Simula/on' Procedures'Without' Connec/ons' Drill' Reference' Out$of$Context$ In$Context$ Procedures'With' Connec/ons' Based'on'Stein'and'Smith'(1998)' Memoriza)on+

6 The encyclopedia Teaching Resources PDF!

7 100+ page ebook available at

8 Common Core State Standards

9 Algebra Card Clutter Help students develop understanding of the relative values of numeric expressions. Misconception: students have difficulty understanding the relative values of integers. Task: Pick up the cards in order, starting with smallest. The clock is running.

10 Other apps for developing number sense Math Snacks: Pearl Diver Math Tappers: Numberline

11 Hop the Number Line Developing number sense Number lines are semiconcrete models that students can use to make problems countable Builds a durable measurement model for addition and subtraction for whole numbers, fractions/ decimals, and positive/ negative integers.

12 Tortoise and the Hare (rate of change) Can you run the race with the tortoise finishing in 20 seconds and winning? Extension: What are the values for the hare that result in the closest win?

13 Action Grapher Shodor.org Misconception: the graph always looks like the hill or the flask. What do we mean by rate of change? Tip: sleep/home to capture solution for math journal Action Grapher (under Doodle send screenshot to:

14 Cover Up Cover Up helps students develop a strategy for solving algebraic equations that is more intuitive than a mechanical use of order of operations. Beyond a procedural understanding and toward a conceptual understanding See instructions in the app for more...

15 Point Plotter Misconception: only integer points between two points on a line vs. an infinite series of points Develops students sense of relationship between points

16 Submariner Algebra Develop students understanding of points on a line, slope, and y-intercept with this game environment. Similar to the game Battleship, students graph submarine paths (3 lines) for a competing student to find. Dropping depth charges (x,y points), students seek the submarine paths. After a couple of hits, students use the points to identify the equation of a line to determine if they have found one of the submarine paths.

17 Math Flyer Explore the relationship between m & b in y=mx+b parallel & perpendicular Slope Slider (free) as well, but only for straight lines Shodor.org

18 Algebra Tiles for factoring and solving Visual representations help students develop conceptual understanding of algebraic topics. Algebra Tiles help students represent and solve algebra problems using tiles to represent variables and constants.

19 Algebra Equation Builder students struggle to understand the nature of the equal sign, an essential idea in algebra.

20 Students have difficulty in algebra understanding the equal sign as a balance between two equal expressions. This app: Using tiles you can take away something from both sides of the equation. It features a balance beam scale with colored objects (that correspond to numbers in the equation) that allows the user to remove equal objects simultaneously to help visualize simplifying equations. The user is given an equation in two different forms: one with numbers, the other in colored objects. The user can remove equal objects from both sides until it cannot be simplified further to get the answer to the numbered equation. There is also a place to enter answers and have them checked. There are multiple levels of increasing difficulty including things such as parentheses, fractions, and multiple variables.

21 Inequality kickoff Help students understand the meaning by using inequalities on a number line. Students have significant difficulty understanding which direction to shade lines and the meaning of that shaded line. They struggle to understand how values work in an inequality.

22 Linear Model view multiple representations simultaneously view dynamic of changing axes intervals

23 Diamond Factor Practice factoring quadratic equations Decimals used instead of fractions

24 Lion Grapher Write an equation to get a line into the lion s mouth Develop student understanding of slope and y- intercept. Construct meaning for all aspects of linear equations

25 Function Mystery Machine Look for patterns in order to figure out the function Try out the two player version with a neighbor

26 New and coming apps Compounding interest simulator (new) Algebra Equation balancer (new) Distance=rate * time formula simulator Graphing a parabola (Math Flyer like)

27 Teaching Algebra for Understanding with Virtual Manipulatives on ipads Dr. Mike Charles Dr. Linda Samek Pacific University Oregon Dr. Rachel Harrington Dr. Steve Rhine

28 Tell us what you think! There are two ways to provide feedback on this session: ISTE 2014 mobile app isteconference.org/feedback