Algebra Tiles Using Algebra tiles to support students conceptual understanding Algebra Tile Overview Conceptual Understanding through Manipulatives in K-5 Conceptual Understanding through Manipulatives in Middle Grades Making zero Pairs Model a word expression

Build strong math vocabulary Distributive property Apply properties to make equivalent expressions Solve one-variable equations and inequalities Achievethecore.org K-8 Progression Base Ten Blocks K-4

One one hundred Three tens Two ones 132 100+30+2 Activate and Connect

7 = 3x - 8 Connecting Concepts Math Framework Grade 4 Multiplication Arrays Math Framework Grade 3 Tape Diagram/ Comparison Mat

Connecting Concepts Math Framework Grade 5 Decimal Multiplication Arrays Math Framework Grade 6 Examine Rational Numbers and their Opposites

Framework at a Glance Grade six marks a foundational year for building the bridge between concrete concepts of arithmetic and the abstract thinking of algebra. Visual representations and concrete models (such as algebra tiles, counters, and cubes) can help students develop understanding as they move toward using abstract symbolic representations. - Privately Read Middle Grades at a Glance Handout. - What do you notice about the progression of ideas?

- What strikes you? - Form a Triad: Algebra Tiles Solidify the Zero Pair with Tiles 1

+ (-1) = 0 3 + (-3) = 0 Grade 6 Standard

Algebraic Mats Expression Mats Equation Mats http://bit.ly/algebratilemats Integers - Use of Expression Mat Uses might include:

What is 5 + 4 Making zero Pairs (G6M3,G7M1) What is 6 - 3 (zero pair) Model a word expression

Write a zero pair number sentence Build strong math vocabulary What is -2 + 5 Integer addition and subtraction (G7M1)

What is (-5) + (-4) Integer Multiply and Divide What is -6 - (-2) Distributive property Apply properties to make

What number sentence describes the model? Use of Expression Mat Uses might include:

What number sentence describes the model? Model Six times a number less three Making zero Pairs

Model a word expression(G6M7, G7M6,G8M7) Build strong math vocabulary (G6M7) Integer addition and subtraction Integer Multiply and Divide Distributive property (G6M7,G7M6, G8M7)

Build 2x - 3y + 5 on your mat. -Identify the operation -Identify the number of terms -Identify the variables, their coefficients -Identify the constant Build (x+3), build another (x+3) Build the expression 7x - 21 in 2 ways Use of Expression Mat

Uses might include: Making zero Pairs Model a word expression What is (-3)(-4): the opposite of 3 sets of -4 Build an expression 7x - 3 Simplify (3x+1) + (2x-7) Build strong math vocabulary

Integer addition and subtraction Integer Multiply and Divide (G7M2) Distributive property (G6M7,G7M6, G8M7) Apply properties to make Simplify 5 + 3(x + 1) - 7x What number

sentence describes the model? Use of Comparison Mat Uses might include: Making zero Pairs Model a word expression

Find an equivalent expression to 2(2x4)+3 Write an equivalent expression for (3x + 1) + (2x -7) Build strong math vocabulary Integer addition and subtraction Integer Multiply and Divide Distributive property Apply properties to make

equivalent expressions (G6M7,G7M6, G8M7) Which is greater? 2x+8-x-3 or 6+x+1 Model the inequality and find 3 possible solutions for 6x - 4 > 8 Use of Equation Mat

Use of Equation Mat A Uses might include: Making zero Pairs Model a word expression Build strong math vocabulary Integer addition and subtraction Solve 3x - 2 = 7 Solve 2x + 4 = 5

Solve 2x + 10 = 38 Solve -3x + 4 = 5 Integer Multiply and Divide Solve 2x + 10 = 38 Distributive property

Solve x + 5 = 3x - 1 Apply properties to make equivalent expressions Solve x + 4 = -x - 4 What number sentence

describes the model? Integers - Use of Equation Mat B Uses might include: More deeply explore multiple terms and operations on each side of an equations

Solve 3(x - 5) + 1 = 2 + x Solve 3x -2(5x + 3) = 14 - 2x What number sentence describes the model? What if...

The equation isnt written yet? Concrete Representational Abstract

Progression before Middle Grades Progression before Middle Grades Progression before Middle Grades Progression before Middle Grades 3+ 2 =5

Progression before Middle Grades Go Math Grade 3 Progression before Middle Grades Go Math Grade 4 Progression before Middle Grades Go Math

Lorkich picked 3 times as much corn as Ethup. Progression before Middle Grades Go Math Lorkich picked 3 times as much corn as Ethup. Together, they pick 96 ears of corn.

Progression before Middle Grades Go Math Lorkich picked 3 times as much corn as Ethup. Together, they pick 96 ears of corn. Ethup wants to divide the number of ears she picked equally among 8 bags. How many ears of corn will Ethup put into each of the 8 bags?

Sample Task from SBAC Grade 6 A recipe requires cup of flour for every batch of cookies. How many full batches of cookies can be made with 5 cups of flour? Sample Task Allan puts some brown sugar on a dish. The total weight of the brown sugar and the dish 110 ounces. Bella puts three times the amount of brown sugar as Allan did, on an identical dish. The total weight of Bellas brown sugar and the dish is 290 ounces.

Find the weight of the brown sugar that Bella puts on the dish. Sample Task Allan puts some brown sugar on a dish. The total weight of the brown sugar and the dish 110 ounces. Bella puts three times the amount of brown sugar as Allan did, on an identical dish. The total weight of Bellas brown sugar and the dish is 290 ounces. Find the weight of the brown sugar that Bella puts on the dish.

Partner Time: developing equations from bar models Using a Diagram Related Equations Partner Time: developing equations from bar models Using a Diagram

Related Equations What questions could be asked to get kids started? What questions could be asked about the bar diagram that help students make connections to the context? Notice... and Wonder... Taira and Meredith each had the same amount of money. Taira spent $58 to fill the

car up with gas for a road-trip. Meredith spent $37 buying snacks for the trip. Notice... and Wonder... Taira and Meredith each had the same amount of money. Taira spent $58 to fill the car up with gas for a road-trip. Meredith spent $37 buying snacks for the trip. Afterward, the ratio of Tairas money to Merediths money is 1:4 . What Math Questions could be asked? Taira and Meredith each had the same amount of money. Taira spent $58 to fill the

car up with gas for a road-trip. Meredith spent $37 buying snacks for the trip. Afterward, the ratio of Tairas money to Merediths money is 1:4 . What Math Questions could be asked? Taira and Meredith each had the same amount of money. Taira spent $58 to fill the car up with gas for a road-trip. Meredith spent $37 buying snacks for the trip. Afterward, the ratio of Tairas money to Merediths money is 1:4 . Question for us: How much money did each have at first?

HMH Online Algebra Tiles Questions? Advantages? Challenges? Where can you see these ideas being used in your classroom?