Algebraic Thinking

Math Playground: Algebraic Reasoning

source: http://www.mathplayground.com/algebraic_reasoning.html

Materials: 

• computer that can run the game

Directions:

• students should go to http://www.mathplayground.com/algebraic_reasoning.html 
• then they can select the difficulty level of the problems that they want to do
• then they are given pictures like these and they have to use the information they are given to solve the unknown

• 
  

Algebraic Thinking - Calculator (2)

Broken Calculator: can you fix it?

source: source: Elementary and Middle School Mathematics: Teaching Developmentally by John A. Van De Walle, Karen S. Karp, and Jennifer M. Bay-Williams. Activity 14.11

Materials:

• calculators

Directions:

• ask students if they can make the calculator display an even number without using any of the even keys (0,2,4,6,8).  If they can, ask them to explain how.
• Next ask students if they can make the calculator display an odd number without using any of the odd keys (1,3,5,7,9).  If they can, ask them to explain how.
• then ask students for conjectures they can make about odds and evens based on their explorations

Operations Toss:

source: www.dixax.com

Materials:

• dice
• pencils
• calculators
• handouts pictured below

Directions: 

• Each team tosses a die, higher number goes first
• Each team chooses a color token

To play:

• Toss a red die and a green die. Red die = n; green die = y.
• On the Operations Toss recording chart, compute (2n)2 + y or 2n2 + y.
•  Choose either solution, and place a token on the solution on the chart below.
• The opposing team must agree to your solution.
• After 10 tosses, each team tallies the numbers under their tokens.
• The team with the higher score wins. 

Algebraic Thinking

balls, balls, balls

source: Elementary and Middle School Mathematics: Teaching Developmentally by John A. Van De Walle, Karen S. Karp, and Jennifer M. Bay-Williams. Activity 14.9

Materials:

• paper handouts or an alternate way to distribute ball facts
• paper/pencils for students to work with

Directions:

• students will figure out the weight of three balls, given the facts pictured on the right (baseball + football = 1.25 pounds, baseball + soccer ball = 1.35 pounds, soccer ball + football = 1.9 pounds)

• ask students to look at each fact and make observations that help them generate other facts
• example: noticing that the soccer ball weights .1 lb more than the football
• write facts like this the same way you wrote the other statements
• continue until you have solved the problem :)

Equivalent Fractions

Equivalent Fractions Splat

Source: http://www.sheppardsoftware.com/mathgames/fractions/equivalent_fractions_shoot.htm

Materials:

• Access to computer/tablet that is connected to wifi and can run the game

Directions:

• Have students go to  http://www.sheppardsoftware.com/mathgames/fractions/equivalent_fractions_shoot.htm (also found by going to sheppardsoftware.com, clicking math games, then scrolling down to the fractions heading and clicking on equivalent fraction splat)
• students can then select their difficulty level - the teacher might need to encourage students to start out with the easier level before moving to the harder level
• Students will be given a written fraction on the mouse/shooter and they will move it around and use it to click on the picture of the equivalent fraction

Estimating Fractions

Estimate Fractional Shapes

Source:  http://www.sheppardsoftware.com/mathgames/fractions/EstimateFractionsShapesShoot.htm

Materials: 

• access to computer or tablet that is connected to wifi and can run the game

Directions: 

• Students go to http://www.sheppardsoftware.com/mathgames/fractions/EstimateFractionsShapesShoot.htm or go to sheppardsoftware.com then click on math games - estimation (on the left side) then they should scroll down to estimate fractions (right column)
• next students play the game - 

Game Description: Students are given a collection of regional fractions and a numerical fraction and they have to estimate which shapes have the fraction that they are given have the appropriate fraction shaded in

Fractions (measurement)

A meter of candy

source: http://illuminations.nctm.org/

materials:

• Candy 
• Meter-long strips of paper
• Meter sticks
• Crayons, markers, or colored pencils
• Posterboard
• Tape
• A Meter of Candy Overhead 
• A Meter of Candy Activity Sheet 
• Grids Activity Sheet 

Directions: 

• split students up into groups of 2 or 3 and have them line up their candies against a meter stick
• ask the students if they can easily tell what percentage/fraction of candy is a certain color
• ask students how they would be able to tell more easily
• then color by the meter stick so that they can see where the colors were when they lined up the candies and the meter stick
• next have them line the candies up on a hundred grid
• and color the hundreds grid so that they can compare it to the meter stick
• students should be talking about percentages as well as fractions during this activity

 

Fractions (as part of a region)

Playground Fractions

source: Elementary and Middle School Mathematics: Teaching Developmentally by John A. Van De Walle, Karen S. Karp, and Jennifer M. Bay-Williams.

materials:

• Pattern blocks
• grid paper for students to record on

directions:

• show students the picture of the "playground" and have them recreate it.
• Then have them use pattern blocks to find different fractions listed and draw them on their paper

Fractions (as part of a set)

Matching Fractions

Source:  Matching fractions in a set game from Sheppard Software http://www.sheppardsoftware.com/mathgames/fractions/fractionSet.htm

Materials: 

• ·      access to a computer or tablet that can load the game
• ·      access to internet

Directions:

• ·      After doing work with fractions so students have some understanding of fractions within a set tell students to follow this link:
• ·      http://www.sheppardsoftware.com/mathgames/fractions/fractionSet.htm
• ·      or have them go to sheppardsoftware.com and then click on math games and scroll down to fractions to find matching fractions in a set

Multiplication and Division Activity

Multiplication and Division: How to Solve? 

Source: Elementary and Middle School Mathematics: teaching developmentally by John A. Van De Walle, Karen S. Karp, and Jennifer M. Bay-Williams. Activity 13.5

Materials:

• Problems which are reasonably difficult for students’ current skills
• Such as: “T-shirts with the school logo cost $6 wholesale.  The Pep Club has saved $257.  How many T-shirt’s can they buy for their fundraiser?”
• Whiteboards or paper for students to scribble on so that they can share ideas if they want to keep a record of their thinking

Directions:

• The task is to give students a problem and have them describe the steps they would take to solve the problem (not actually solving it)
• Then have students share ideas

Division Activity

Candy Capers

Source:

http://www.fun4thebrain.com/Division/candycapersdiv.html

Materials:

• Computer or device that connects to Internet and has adobe flash capabilities
• Headphones for students if they want to use music

Directions:

• Have students go to http://www.fun4thebrain.com/Division/candycapersdiv.html to play candy capers
• Students can select the fact families they want to work on (two through twelve)
• Then students play through the game avoiding cats that try to steal their candy – they can get candy by correctly answering division questions

Multiplication Activity

Multiplication Fact Origami

Source:

·      http://vintagetoysblog.wordpress.com/2013/02/25/paper-fortune-teller-free-printable-template/ (for how to make the fortune teller)

·      http://luv2teachgirl.blogspot.com/2011/05/math-differentiation.html via Pinterest for the actual math related part of the activity

Materials:

·      Paper

·      Markers

·      Scissors

Directions:

•       First, follow the directions on the template to make fortune tellers (on next page)
•       Then have students label the fortune teller with multiplication facts that they need extra practice with and fill in the answers underneath the flaps
•       Play