Download CY_Math_201 - CYC Academics Wiki

Do Now:
Mental Math String
• Please do the Mental Math String
found in your packet
•
Perform all steps mentally, but please write
down ONLY your final answer
• If you finish before we start try
making your own string on the
blank side of the paper
CITY YEAR CHICAGO
Math 202
Session Developer: Mari Mermelstein
City Year Chicago
Overview
• What Are You Seeing?
• Revisit common student struggle
• Computational Fluency – what is it?
• Online Worksheet Generators
• Fact Families/Basic Operations
• Fractions!!
• Decimals and Percents
• Averages
• Exponents
• Math Games
Math Anxiety
• Weak Computational
Skills
• Poor conversation or
academic language
skills
• Lack of Confidence
• Unable/Unwilling to
write out complete
solutions
• Weak Conceptual
Understanding
•
Poor test-taking skills
• Low Work Completion
Rate
• Poor English Language
Skills
Weak Computational Skills
What this looks like
Recommendations
-Select practice problems with
addition, subtraction,
multiplication and division facts
the student has mastered so the
focus is on new skill or concept
development.
Student gets bogged down with
“basic” addition, subtraction,
multiplication, and division while
solving more complex problems.
Student gets frustrated because
it takes so much time and
-Work a problem backwards by
energy to solve problems the
teacher/curriculum expects they giving the correct solution and
having the student explain the
know automatically.
process to get the solution.
Weak Conceptual Understanding
What this looks like
Student has a hard time
understanding when to use a
procedure. Student is not
able to explain why a
procedure works or to use it
in a novel situation
Recommendations
-CMs should provide clear
models for solving a problem
type using an array of
examples.
-The student should be
provided with opportunities
to hear instructors think
aloud (talk through the
decisions they make and the
steps they take) when solving
problems.
Low Work Completion Rate
What this looks like
Recommendations
Student is unorganized and
does not turn in completed
assignments.
- AND/OR -
-Create a checklist for
daily/weekly assignments and
help the student prioritize
assignments.
Student seems to be working
consistently, but works so
slowly that they do not finish
assignments.
-Use Graphic Organizers to
help student organize work
and use problem solving
conventions.
Lack of Confidence
What this looks like
Student is easily frustrated.
Student has trouble starting
to work on grade-level
content and consistently
avoids math work. Student
may shut down and will not
attempt to problem solve
even with assistance.
Recommendations
Create authentic
opportunities for success by
focusing on one skill or
concept at a time. Do not
layer skills.
*EX- if introducing the concept of
multiplying with negative numbers
(integers), only use whole numbers
from fact families in which the student
has already shown mastery
Unable/Unwilling to Write Out
Complete Solutions
What this looks like
Student skips key steps.
Student does not write out
the entire procedure
Recommendations
-Have the student do “Think
Alouds” to determine if the student
understands all of the problem
solving steps or if they skip steps
because they do not know them.
-Use graphic organizers or problem
templates that emphasize procedure.
-Give students sufficient time and
white space on paper to write out
the entire problem solving process.
Poor Test-Taking Skills
What this looks like
Recommendations
-Coordinate with the teacher
to focus on high-impact
tested skills during tutoring.
Student may show an
understanding of key
-Allow students to problemconcepts in tutoring session solve independently and give
but does not perform well on
sufficient time for selfclassroom exams.
correction to model the selfmonitoring student will need
to perform during testing.
Poor Conversation or Academic
Language Skills
What this looks like
Recommendations
-Listen to the student read the
directions and problems.
Student has difficulty
understanding what the
-Dissect words to their
directions are asking the
student to do and has difficulty mathematical root to help the
understanding word problems. student comprehend the
mathematical meaning of the
Student does not use
original word.
appropriate academic language
-Use vocabulary focused
and does not show an
graphic organizers or pictures
understanding of grade
as visual tools to aid the
appropriate academic
student in thinking about
vocabulary when read.
mathematical language.
Poor English Language Skills
What this looks like
Recommendations
Student is not able to read
and understand the text.
-Read mathematical text with
(or for) the student and
discuss meaning of academic
words.
Student has difficulty
understanding academic
language used in class.
*Student might be
mathematically proficient in
another language.
-Draw a picture or model to
depict problem (when
appropriate).
-Use easier numbers in
problem sets.
Math Tutoring
Computational Fluency
• The ability to efficiently and accurately compute addition,
subtraction, multiplication and division problems
• Focus on Whole Numbers and Fact Families
• Advance Computational Fluency will
focus on Commutative, Associative,
and Distributive Properties
• Number One Rule…
…No Calculators!!!!
Mental Math Strings
Challenges students to perform calculations mentally
Formative
Assessment Tool:
•Practice mental math skills
•Assess student knowledge
•Gauge student learning
• Any number of steps
• Steps can either be a
calculation or a number fact,
i.e. Start with the largest 2
digit whole number
• Be sure calculations are skill
level appropriate
Online Worksheet Generators
Website
•
The Math Worksheet •
Site
•
(very good for Fact
•
Families practice)
•
http://themathworksheetsite
•
.com
•
Skills
Problem Sets
Addition*
Subtraction*
Multiplication*
Division*
Mixed Facts≠
Fractions±
Graph Paper
*Single Digit (→ or ↓)
• +,-,×,÷,
Superkids – Math
•
•
http://www.superkids.com/a
•
web/tools/math
•
•
Intervention Central
•
(has literacy tools also!)
•
http://www.interventioncent •
ral.org/index/php/tools/196- •
cbm-math-worksheet•
generator
Mixed
Order of Ops
Fractions
Percents
Averages
Exponents
Addition
Subtraction
Multiplication
Division
Mixed Facts
Can specify #s used
*Multiple Digit
*5 Minute Drill
≠Choose Operations
±LCM & Reducing
(choose difficulty and to
include Improper fractions)
Control over:
•Min value
•Max value
•One number in all
•Level of difficulty
Less control over
exact digits used
More control over
EXACT type of
problems (i.e. # digits in
each term and regrouping)
Number of
Problems
Can choose length
of problem set
90 problems
generated for 5
minute drill
Can choose length
of problem set
(Length varies
depending on concept)
Quick Tip
Worksheets
Can choose length
of problem set
Answer sheet
automatically
created
Fact Families
Order of Operations
Order of Operations
Leave-Change-Opposite (LCO)
Apply when subtracting numbers
it turns subtraction problems into addition problems
Order of Operations
Multiplying and Dividing with Positive and Negative
Numbers
TWO positives equal a ____________
ONE positive and ONE negative equal a ____________
TWO negatives equal a _____________
Fractions - Reducing
Fractions – Least Common Multiple
Fractions – Common Denominators
4, 8, 12
6 , 12
Fractions
Addition
Division
Average
ADD all the terms together
and DIVIDE by the
number of terms there are.
Exponents
x Exponent
B
Base
4
2 =2×2×2×2=16
Decimals & Percents
Decimals and Percents
D→P
Multiply by 100
P→D
Divide by 100
Math Games
All of these games can be played before school, during T2
tutoring sessions, or during After School Homework Help
•Who’s got 1
•Card Multiplication
•Math Power Cards
•Variable Math War
•Rolling 100
•First to 100
•Add it Up
•Ball Toss
•Prime Factor Relay
Math Power Cards
1
2
3 4
5
6
7
8 9
• Skills: Addition with multiple digits and logic
• Set Up: 9 index cards labeled 1-9 per 2 students
• Goal: Use 3 index cards to add to 15
• Process: 1) Nine cards are randomly laid face down on the table.
2) Students alternate picking up one card at a time.
3) First student to find three cards that add up to 15 wins!
• Variations: Give a set of 9 cards to each student or team. See how
many 3 card combos they find to add up to 15 in a given amount of
time. (*8)
Use 5, 12, 19, 26, 33, 40, 47, 54, 61 to find 3 card combos
that sum to 99.
Who’s Got 1?
• Skills: Adding fractions with unlike denominators
1 5 1 7 1 3 5 11
1
, , , , , , , and
6 24 4 24 3 8 12 12
2
• Set Up: 9 index cards labeled ,
per 2 students
• Goal: Use 3 index cards to add to 1
• Process: 1) Nine cards are randomly laid face down on the table.
2) Students alternate picking up one card at a time.
3) First student to find three cards that add up to 1 wins!
• Variations: Give a set of 9 cards to each student or team. See how many 3
card combos they find to add up to 15 in a given amount of time. (*8)
Add It Up
• Skills: Addition with 1-4 digit numbers
• Set Up: Paper and pencil. 2-25 students
• Goal: Add to the highest number in one minute
• Process: 1) The leader will announce a number and an addend.
For Example: 7 and 4.
2) Students write and add the two numbers and continue to
add the same addend to the new sum until the leaders calls stop at the
end of one minute .
3) Group stands and a volunteer begins slowly reading
problems and answers aloud.
4) As students no longer have the answer, they sit down
5) The student left standing wins!
• Variations: Try subtraction, 2 or 3 digit numbers, or negative numbers
Ball Toss
•
•
•
•
Skills: Patterns, skip counting, +, –, and ×
Set Up: 1 ball (or tossable item – NOT A STUDENT ), 4-12 students
Goal: Work together as a group to see how high you count
Process: 1) Get the group in a circle. The leader explains that they will be
tossing a ball to one another. The students will need to remember who tossed
to them and who they toss the ball to.
2) The leader will then toss the ball to a student, who then tosses it
to another student. Continue doing so until the ball has reached everyone, with no
repeats. The last person will toss the ball to the leader.
3) The leader will pick a starting number (like 2) and tells the group
what number to add to each toss (like 3).
4) The leader calls out 2 and tosses the ball to the SAME person
they tossed the ball to before. That person says 5 and tosses to the next person
and so on… the counting pattern would be 2, 5, 8, 11…
• Variations: Try sub or mult, or if you mess up you are out - the person after
you will choose the starting number and adding amount.
First to 100
• Skills: Addition, reasoning, and logic
• Set Up: Pencil and paper (optional), 2 students
• Goal: Be the person to say 100.
• Process: 1) Player one starts by saying a number between 1 and 10.
2) The next player says a number that is up to 10 numbers higher
than the previous number.
3) Alternate turns until one player wins by saying “100”.
• Variations: Start with 100 and have students subtract to get 0. Have
a discussion about whether to win it matters if you go first or second.
Rolling 100
• Skills: Addition with 2 digit numbers
• Set Up: Two dice per group, pencil and paper
2-6 per group
• Goal: Be the highest scorer after 10 turns or be the first player to
reach 100.
• Process: 1) Players take turns rolling the dice.
2) Each player may roll as many times as they want adding
up the numbers rolled. If the player roles a one, he or she loses all points
accumulated during that turn. If the player roles a one on both of the dice,
he or she loses everything and starts over with zero.
3) If the player stops his or her turn before throwing a one,
then he or she passes the dice to the next player and records the total
score for that turn.
Card Multiplication
• Skills: Multiplication with 2 digit numbers.
• Set Up: 1 Deck of cards and 1 or 2 dice per group, 2-8 students/group
• Goal: Be the first to get 10 points!
• Process: 1) The leader or a student will roll the dice. That number is the
multiplier for the round.
2) The leader flips a card over to students one at a time.
3) Students multiply the number value of the card by the multiplier.
Students earn a point if they get the answer correct.
4) All face cards are valued as 10 and aces are 1.
5) Once a card has been presented to each student, roll the dice to
get a new multiplier for the next round.
6) The first students to get 10 points wins
• Variations: Give the face cards higher values (J=11, Q=12, K=20). Students
go head-to-head: student who says the answer first gets the point.
Example
• Leader rolled a 2 and a 5, so the multiplier
for this round is 7.
Variable Math War
• Skills: Substitution and Simplification of expressions.
• Set Up: 1 Deck of cards per pair of students
• Goal: Get all of the cards!
• Process: 1) Split the deck of cards evenly.
2) Assign one student the x-value and one the y-value.
3) When the students flip their cards they must do so at the
same time and lay their cards down in full view of the other player.
4) Start the game by writing an equation in the form of
z = Ax + By, where A and B are any integer number (positive or negative).
5) Once cards are flipped, students substitute the face value of
the cards into the equation and determine what z equals.
6) The first student with the correct answer collects both cards.
• Variations: Give the face cards higher values (J=11, Q=12, K=20).
Adjust
the difficulty: Easier - Change the equation to z = Ax + Bx, where the
student’s card values substitute in for the coefficient (A and B) - a game of
combining like terms. Harder - Change the equations by making A and B
fractional coefficients, adding exponents or more terms.
Example
z = 2x + 3y.
x
y
Prime Factor Relay
• Skills: Prime Factorization
• Set Up: Chalk board and chalk or dry-erase board and markers. 3-4
students in 2-4 groups
• Goal: Be the first team to correctly factor the number
• Process: 1) Students line up facing the board.
2) Leader will announce a number, and Player 1 (P1) will go to
the board, write the number, and draw two lines for the next person, return to
the line, and pass P2 the chalk/marker.
3) P2 goes to the board and writes down two factors of the
original number, then passes the marker to P3.
4) P3 lists the factors of the numbers P2 has written – this
continues until the prim factorization has been found.
5) Players must circle the prime numbers they write.
6) The first team to write out the prime factorization wins!