The Algebra ClanMom, Pop and all the Relatives

Border tile problem

TableMake a table showing the numbers of blue

tiles for water and white tiles for the border for the first six square pools.

What are the variables in the problem? How are they related? How can you describe this relationship in words?

GraphMake a graph that shows the number of blue

tiles in each square pool. Make a graph that shows the number of white tiles in each square pool.

As the number of the pool increases, how does the number of white tiles change? How does the number of blue tiles change? How does this relationship show up in a table and in the graph?

Use your graph to find the number of blue tiles in the seventh square.

Patterns & GeneralizationsCan there ever be a border for a square pool

with exactly twenty-five white tiles? Explain why or why not.

Find the number of blue (white) tiles in the 10th pool. The 25th pool. The 100th pool.

If there are 144 blue squares, what is the side length of the square pool including the border? How many white tiles are needed for the border?

Algebraic ReasoningWhat are the variables in this situation?

What quantities are changing?How are the variable related?As one variable increases, what happens to

the other variable?How can you represent this relationship

using words, concrete objects, pictures, tables, garphs or symbols?

How can you build connections among representations?

How can you use this relationship to predict information about the variables?

Draining a swimming poolExpressions vs. EquationsHow does knowledge of ratios

and proportions enter into this?Purple tiles to green tiles; other

proportion problemsWhat’s the learning progression?

Knots in a RopeCollecting real dataWhat questions can be asked

about this?What expressions and equations

can be written, and what questions do they answer?

What kind of graph can be drawn?

The Cruise ShipTime Distance cruise

shipDistance speed boat

0 hr 0 miles 0 miles

1 hr 20 miles

2 hr 40 miles

3 hr 60 miles

4 hr

5 hr

7.RP.2 b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

In small groups, determine an approach

Gas Mileage – just for fun

Whose car had the largest gas tank?

Whose car ran out of gas fist?Whose car went farthest (at

same speed)Whose car got worst gas

mileage?

What’s the family tree?Using the Common Core

Collaborative Cards, find your group and arrange the cards to show connections.

Function

Table

Graph

Equation

Solving equations with integers-8x + (-2) = -5xWhat the heck does it take?

Authentic situations involving negative numbersThermometer ProblemsElevator ProblemsHappy and Grumpy PeopleHot and Cold CubesBiking Across Town

Where does this leave us?What are the big questions

you’re grappling with?

Teaching PracticesFeldman observation formIES Practice GuideHow many times in a week do

you do each of these? 0-3, 4-10, more?