CONSTRUCTING AND DECONSTRUCTING FOR ALGEBRA READINESS Andrea Tamarazio & Steve Graser, Erie 1 BOCES...

CONSTRUCTING AND DECONSTRUCTING FOR

ALGEBRA READINESSAndrea Tamarazio & Steve Graser , Erie 1 BOCES

April 9, 2013

Algebra Warm Up

Complete the Frayer Model independently then create a final table version.

Post the table Frayer Model along the wall.

Algebra Vocabulary Brainstorm

Does This Help?

Will This Help?

How Can This Help?

Will This Help?

Nomials

3xy2

5x - 1

3 x + 5y2 - 3

Expression vs. Equation

2x – 6

2x – 6 = 5

Write Algebraic Expressions for The Word Phrases

A number s plus 2

A number decreased by 1

31 less than a number

A number b increased by 7

The sum of a number and 6

Scott’s brother is two years younger than Scott

Write Algebraic Expressions for These Word Phrases

A number s plus 2 s + 2

A number decreased by 1 n - 1

31 less than a number n - 31

A number b increased by 7 b + 7

The sum of a number and 6 n + 6

Scott’s brother is two years younger than Scott s - 2

Show Me

eighteen

Compare 24 and 15

One less than thirteen

Two numbers that make 20

Three numbers that make thirty-seven

The sum of nine and twelve

Bar Diagrams / Tape Diagrams

Part Whole Model

Comparison

Why Learn Algebra

Learning Algebra

All students should learn algebra beginning in pre-kindergarten

“By viewing algebra as a strand in the curriculum from pre-kindergarten on, teachers can help students build a solid foundation of understanding and experiences as preparation for more sophisticated work in algebra in the middle grades and high school.”

NCTM, 2000

Primary algebra should not be a watered-down version of the standard high school course that most of us took; instead the goal in Grades K - 2 is to develop students’ understanding for the order and situations, predict beyond the information at hand, and make generalizations.

from Lessons for Algebraic Thinking Grades K- 2 by von Rotz and Burns

Algebra Experience?

Students in Grades K - 2 have knowledge about and are developing comfort with number patterns

Patterns provide a useful foundation on which teachers can develop students’ algebraic thinking

Students need experience creating, recognizing, and extending patterns Relating to items in which they are familiar with This foundational skill leads to the conceptual

understanding of functions in future years.

from Lessons for Algebraic Thinking Grades K- 2 by von Rotz and Burns

Connecting to CCLS

Looking at your Grade Level CCLS, identify and list which standards connect to foundational skills within algebra.

On Chart Paper, make a grade level list.

NYSED Recommended Models for Algebra Readiness

Area Model / Arrays

Number Bonds


Number Towers

Show me how many groups of four make 24.

Write and solve an equation aligned to the prompt above.

Area Model / Array Example

24

6

X

Array Model Video

http://learnzillion.com/lessons/1876-use-area-models-to-show-multiplication-of-whole-numbers

Area Model

X

y

48

Area Model Video

http://learnzillion.com/lessons/852-adding-mixed-numbers-using-properties-of-operations

Number Bonds

Number Bond Video

http://learnzillion.com/lessons/783-determine-all-multiples-of-a-number-using-number-bonds

http://learnzillion.com/lessons/783-determine-all-multiples-of-a-number-using-number-bonds

Number Bonds


Part Whole Model

ComparisonBar Diagram Video

http://learnzillion.com/lessons/1744-interpret-division-as-an-unknown-factor-problem-using-a-bar-model

http://learnzillion.com/lessons/1744-interpret-division-as-an-unknown-factor-problem-using-a-bar-model

Bar Diagram / Tape Diagram # 1

Sara has 5 stamps. Mark brings her 4 more stamps. How many stamps does Sara have now?

Bar Diagram / Tape Diagram #2

Sara has 16 stamps. Mark brings her 4 more stamps. How many stamps does Sara have now?


Sara brought 4 apples to school. After Mark brings her some more apples, she has 9 apples altogether. How many apples did Mark bring her?


Matteo has 5 toy cars. Josiah has 2 more than Matteo. How many toy cars do Matteo and Josiah have altogether?

Bar Modeling – Key Points

When building proficiency in tape diagraming skills start with simple accessible situations and add complexities one at a time.

Develop habits of mind in students to reflect on the size of bars relative to one another.

Part-whole models are more helpful when modeling situations where you are given information relative to a whole.

Compare to models are best when comparing quantities.

Writing Word Problems with Tape Diagrams

Tape diagrams are well suited for problems that provide information relative to the whole or comparative information of two or more quantities.

Visual fraction models includes: tape diagrams, number line diagrams, and area models.

When designing a word problem that is well supported by a tape diagram, sketch the diagram for the problem before or as your write the problem itself.

Key Points – Tape Diagrams

Use of tape diagrams, as described in the progressions documents provides visualization of relationships between quantities thereby promoting conceptual understanding, provides coherence through standards from Grade 1 through Grade 7, and supports standards for mathematical practice.

Proficiency in the tape diagram method can be developed in students and teachers new to the process through a natural development of problems and representations.

Content knowledge directed by the standards and the progressions is required to provide coherent and balanced instruction.


Jasmine had 328 gumballs. Then, she gave 132 gumballs to her friend. How many gumballs does Jasmine have now?


Jose has 4 paper clips. Harry has twice as many paper clips as Jose. How many paper clips does Harry have?


Jose has 4 paper clips. Harry has twice as many paper clips as Jose. How many paper clips do they have altogether?


William’s weight is 40 kg. He is 4 times as heavy as his youngest brother Sean. What is Sean’s weight?


Jamal has 8 more marbles than Thomas. They have 20 marbles altogether. How many marbles does Thomas have?


The total weight of a football and 10 tennis balls is 1 kg. If the weight of each tennis ball is 60 g, find the weight of the football.


Two pears and a pineapple cost $2. Two pears and three pineapples cost $4.50. Find the cost of a pineapple.


David spent 2/5 of his money on a storybook. The storybook cost $20 how much did he have at first?


Alex bought some chairs. One third of them were red and one fourth of them were blue. The remaining chairs were yellow. What fraction of the chairs were yellow?


Jim had 360 stamps. He sold 1/3 of them on Monday and ¼ of the remainder on Tuesday. How many stamps did he sell on Tuesday?


Max spent 3/5 of his money in a shop and ¼ of the remainder in another shop. What fraction of his money was left? If he had $90 left, how much did he have at first?


Henry bought 280 blue and red paper cups. He used 1/3 of the blue ones and ½ of the red ones at a party. If he had an equal number of blue cups and red cups left, how many cups did he use altogether?


A club had 600 members. 60% of them were males. When 200 new members joined the club, the percentage of male members was reduced to 50%. How many of the new members were males?


The ratio of the length of Tom’s rope to the length of Jan’s rope was 3:1. The ratio of the length of Maxwell’s rope to the length of Jan’s rope was 4:1. If Tom, Maxwell and Jan have 80 feet of rope altogether, how many feet of rope does Tom have?

Exit Ticket

Create a model to represent the CCLS aligned standards that you previously identified at your grade level.

Contact Information

If you have any questions, please do not hesitate to contact us:

Andrea Tamarazio

[email protected]

Steven Graser

[email protected]

mailto:[email protected]

mailto:[email protected]

CONSTRUCTING AND DECONSTRUCTING FOR ALGEBRA READINESS Andrea Tamarazio & Steve Graser, Erie 1 BOCES...

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