Alg1 Lesson 3.1: Introducing Quadratic Functions

Lesson 3.1: Introducing

Quadratic Functions

Obj: 6B, 6C, 7A: I can determine if a relationship is
quadratic based on a numerical sequence whose
indices increase by a constant amount.
EQ: How do I know if a sequence is quadratic?

Roles:
Facilitator
Scribe
Resourcer
Includer

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas and prior info
● Help explain ideas to each other
● Own your ideas and work
● Record ideas in your journal
● Answer Questions on Slides
● Follow your team roles

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Scribe

• Make sure peers organize their results on their own papers.

• Remind peers to use color, arrows, and other math tools to
communicate your mathematics, reasons, and connections.

• Be ready to join the teacher for a huddle.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties
that may arise.

Includer

• Make sure that all peers are talking about their work.

• Helps keep peers’ voice volume low.

• Encourages everyone to ask questions.

• Communicates conflicts or questions to the teacher.

Poll

What is the person next to you gonna do?

• Includer & play snake

• Facilitator & play snake

• Resourcer & play snake

• Scribe & play snake

● Check off tasks & skills on calendar.

● Select skills to work on.

● Work on Deltamath.

Remember to work on the following too…

Part 1: Exploring a
Nonlinear Sequence

Suppose that you are building with LEGO bricks and want
to continue the staircase pattern, using only single bricks,
as shown in the picture. If you want to build a staircase
that is 10 bricks tall, how many total bricks would you need
to build it?

Fill in the Blank

If you want to build a staircase that is 10 bricks tall, how many total
bricks would you need to build it? ___ bricks

Multiple Select

What are the two quantities in this problem?

• height of the staircase

• number of bricks needed

• the material of the bricks

• the width of the bridge

Drag and Drop

We can think about this like a function because a staircase of a given height will be associated with ​

Placeholder

amount of bricks.

We could use the ​

Placeholder

as the input and the ​

Placeholder

as the output. If we know ​

Placeholder

, we will be able to determine​

Placeholder

.

Drag these tiles and drop them in the correct blank above

only one

height of the staircase

number of bricks

how tall we want the staircase

how many bricks we need to build it

a changing

The height of the staircase is h and the total
number of bricks to build the staircase is b(h).

This is a quadratic sequence since the
second difference is constant. Quadratic
sequences have a linear rate of change.

Word Cloud

What is your favorite game?

Part 2: Playing Snake

Snake

The video game Snake has been around for decades. In fact, Nokia,
the manufacturer of one of the first affordable cell phones,
included the game on every phone. Snake is simple. You control a snake that
never stops moving around the screen, and you must prevent the snake from
hitting itself or the edges of the screen. In one version of the game, the snake
starts off being five units long. As you move around eating small pieces of food at various places on the screen, the length of the snake grows.

Go to https://g.co/kgs/Thb4YsL

to play snake. Who can get a

higher score than 40?

My high
score for this
iteration of
Snake.

a) In round 1, the snake grows by two units for every

one piece of food. How long will it be after it has
eaten three pieces of food? Seven pieces of
food? Fifteen pieces of food? How would you
describe the snake’s growth?

Round 1 could be modeled by a linear
function. The quantities are the input
could be the number of pieces of food
eaten, and the output could be the length
of the snake. It would be a linear function
because the rate of change is constant.
(The first common difference is 2).

b) In round 2, the length of the snake grows by one

unit after one piece of food; after the second
piece of food, the snake grows by two units; after the
third piece, the snake grows by three units; and so
on. If the snake is five units long to start, how long
will it be after it has eaten three pieces of food?
Seven pieces of food? Fifteen pieces of food? How
would you describe the snake’s growth?

Round 2 could be modeled by a quadratic
function. The quantities are the input
could be the number of pieces of food
eaten, and the output could be the length
of the snake. It would be a quadratic
function because the rate of change is
linear. (The second common
difference is 1).

c) People who played this game often found that it

started off easy but became difficult rather
quickly. Which do you think would be more difficult
to play, round 1 or round 2? Justify your answer.

d) In round 2, the length of the snake grows by one

You have been asked to design round 3. To make
this the most challenging round, what would you
tell the snake to do every time it eats? Explain why
this round would be the most difficult.

Poll

Have you played Snake before today?

• Yes

• No

Part 3: Summary and

Practice

5

6

7

8

Multiple Choice

Choose the correct answer letter.

• A.

• B.

• C.

• D.

Random Question of the Day Time

https://wheelofnames.com/4ke-epz

We’ll spin the wheel as a class

and spend a minute or so

discussing our answers.