Logistics for TLC Team Planning
Name / School / Phone / Preferred EmailRansom Kong / Boulder Creek
Sue Horrocks / Rother
Pam Stephenson / Shasta Meadows
Melody Fowler / Mistletoe
Jody Sherriff / K-12 Alliance
Meeting date/time/location on teaching day: 10/28/08 – 7:30- Shasta Meadows
1st Lesson / 2nd LessonSchool site / Shasta Meadows / Mistletoe
Teacher’s name / Pam / Melody
Time frame / 8:15-9:15 / 10:20-11:20
Time of debrief / 9:15-10:20 / 11:30-2:00
Room for team to meet / Reading lab
Materials Needed for Lesson / Who is responsible?
Small “stickie” tabs, sheet protectors, Jelly Bellies
Fix Clip and Cover game sheet
Headband; x (3) yellow; = (1) green; player form
Expanded strip; 2 (4) blue; 16 (1) lavender; change game directions / Jody
Ransom
Melody
Pam
Who is typing the lesson for the team? Jody
Who is making the student data sheet and making copies? Pam & Melody
Who will invite the principal or other key site/district personnel? Pam & Melody
Conceptual Flow
Multiplication is used in many forms of math, i.e., division, area perimeter, geometry, algebra.
There are different ways to estimate products.
o Increasing the factors will give an over estimate.
o Decreasing the factors will give an underestimate.
Some numbers can be represented using a base number and an exponent.
· Exponential notation is used to represent repeated multiplication of the same number.
· Numbers involving exponents can be written in three different forms: standard form, expanded form, & exponential notation.
Students need a basic understanding that 3 X 5 is 3 groups with 5 in each group.
Students must learn strategies and apply one that works for them to figure out math facts.
Students will have a greater sense of confidence in math if the can recall their multiplication facts quickly.
Understanding the terminology makes it easier to complete word multiplication problems.
Students need to know place and value to be able to check reasonableness of a product.
TLC: Shasta #11
Planning: 10/21/08 Teaching: 10/28/08
Location: Shasta Meadows & Mistletoe
Teaching Times: 8:15-9:15 (Pam) & 10:20-11:20 (Melody)
Lesson Concept: Exponential notation is used to represent repeated multiplication of the same number. There are different ways to estimate products.
Standard(s):
Teacher Does Student Does Concept
Engage #1:Write 24 on the board. Ask: what is the mathematical term for the 2?
Ask a student volunteer to be a base. Give the student a card with the number 2 on it to hold.
What mathematical term is the 4 called?
Place the exponent headband on the student volunteer. What does this 4 mean?
So how many more twos do we need?
Have 3 more volunteers come to the front and give each a card with the number two on it and have them line up behind the first # two. We can’t see those twos, so let’s bring them out and stand side-by-side.
What operation do we do with the four two’s?
Have 3 more volunteers come up and give them each a card with “x” on it and put between each 2.
So what is 2x2 (4); x2 (8); x2 (16) / ESR: it is called the base
ESR: it is an exponent
ESR: it means that there are 4 twos.
ESR: 3
ESR: multiply them / Numbers involving exponents can be written in three different forms: standard form, expanded form, & exponential notation.
Explore:
We are going to play a game that will help to help you understand how to express exponential notation in standard form and expanded form.
Put transparency of Tic Tac Toe star 1 on overhead. You will work with a partner and you each will have 20 squares; each person will have a different color. You will use 2 number cubes. Toss one cube. That number will be your base number. Toss the other cube, use that number as an exponent for your base. Use your recording sheet, write the number in expanded form. Find the standard form for that number and cover it with your colored square. Your partner will use the calculator to check your standard form answer.
Model using a “think aloud” how the partner will use the calculator and how the person whose turn it is will work out the problem.
If your answer is already covered, you lose your turn.
The first player or team to cover a row, column or diagonal is in one of the sections of the board game wins.
Give 10 minutes to play the game. / Play the game / Numbers involving exponents can be written in three different forms: standard form, expanded form, & exponential notation.
Explain #1:
Distribute final assessment:
Tommy was given the problem: 43 = ?
Tommy said the answer is 12.
Is he correct? Explain and show your reasoning. / ESR: Tommy is not correct. The answer is 64 because it is 4x4x4, not 4x3. / The exponent tells how many times to multiply the base number by itself.
Engage #2:
There are 504 starships with 87 storm troopers in each ship. Using mental math, which would be the best estimated answer and why? (a) 40004;
(b) 45000; (c) 43,848 (answers written on board)
Ask: Who thinks 40004 is the best estimated answer? Count the number of hands and record. Do the same with the other two answers. Then ask someone who chose 40004 to explain their reasoning, then one for 45000 and one for 43,848. / With a partner determine the best estimated answer.
ESR: 45000 because 504 is rounded to 500 and 87 is rounded to 90. 90 times 500 is 45,000. / Rounding factors gives an estimated product.
Explore #2:
Now, you will have an opportunity to explore another game that will help improve your multiplying skills.
This game is called Clip and Cover. Show transparency of the one star game sheet of clip and cover.
Explain and model, using the “think aloud”, how to play the game.
Toss your first number cube to determine which oval on the left where you will start. Mark the oval with the flag. The second toss of the number cube will determine which oval on the right you will use. Mark the oval with the flag.
Round each factor to the nearest 10, estimate the product, find and cover the estimate in the box. Lose your turn if the answer is taken. Your partner will record the estimated factors and the product on the recording sheet and check answers with calculator. The first person to get any 4 in a row up or down or diagonal wins the game.
A couple of easy ways to remember how to round. “5 or more, raise the score; 4 or less, let it rest”. Or make a large upside down “V” on the board (a mountain), put a 0 at the bottom on the left, a 5 at the top, and a 10 at the bottom on the left: 5 or more goes to 10, 4 or less goes to 0.
When you are done with the game, you may re-play the same game or take the challenge on the other side. Show transparency of the 2 star game. This game is similar but you only use one number cube. It is the reverse of the 1st game. You must determine what the original numbers might be.
Give 10 minutes to play the game. / Play the game / Rounding factors gives an estimated product.
Explain #2:
Distribute the assessment paper. Explain directions
Review the math problems on the left and write the number of the compatible math problem.
a) 23 x 32 ___ 1) 20 x 300
b) 419 x 296 ___ 2) 20 x 30
c) 18 x 304 ___ 3) 400 x 300 / ESR: a = 2; b = 3; c = 1 / Rounding factors gives an estimated product.
** Notes: We discovered that when doing exponents the students did the following (and need some focused intervention):
14 = 1 x 1 x 1 x 1 = 4 when a teacher said to the student “What is 1 x 1 ? the answer was 1, then x 1?, the answer was one; by continuing in this manner the student would say “Ohhhh” and quickly change their answer. We continued to then ask, “What about 123 ?” and they would answer 1; we did this several times until they understood that 1 to any power is 1.
41 = 4 x 1 61 = 6 x 1 the students became confused as to how to write any number in expanded form when it is the power of 1
enVision Games
Team Work
· Work in 2’s or 4’s
· Multi steps
· Read problem aloud
· Solve/write
· Explain & prove
· Revise if necessary
Toss & Talk
· Use number cubes
· Explain/answer question
· Need four connected rectangles to win
Think Together
· Given a question
· Four answer choices
· Explain answer choice
Clip & Cover
· Use number cubes, paper clips, tiles
· Answer questions
· Cover answers
· Four in a row to win
Display the Digits
· 1 or 2 players
· paper, pencil
· 0-9 number tiles
Tic Tac Toe
· paper, pencil, squares (2 colors)
· 2 number cubes
· 2 or 4 people
· row, column, or diagonal to win in any section of gameboard
Name: ______
Compatible Jelly Bellies
Review the math problems on the left and write the number of the compatible math problem.
a) 23 x 32 ______1) 20 x 300
b) 419 x 296 ______2) 20 x 30
c) 18 x 304 ______3) 400 x 300
Name: ______
Know your Exponents
Tommy was given the problem: 43 = ?
Tommy said the answer is 12.
Is he correct? Explain and show your reasoning.