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 CHICAGOCITY YEAR CHICAGOCITY YEAR CHICAGO

Math 202Session 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 Unde

rstanding

• Poor test-taking skills

• Low Work Completion

Rate

• Poor English Language

Skills

Weak Computational Skills

What this looks like Recommendations

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 energy to solve

problems the teacher/curriculum expects they know

automatically.

-Select practice problems with addition, subtraction, multiplication and division

facts the student has mastered so the focus is on new skill or concept

development.

-Work a problem backwards by giving the

correct solution and having the student

explain the process to get the solution.

Weak Conceptual Understanding

What this looks like Recommendations

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

-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 -

Student seems to be working consistently,

but works so slowly that they do not finish

assignments.

-Create a checklist for daily/weekly

assignments and help the student prioritize

assignments.

-Use Graphic Organizers to help

student organize work and use problem

solving conventions.

Lack of Confidence

What this looks like Recommendations

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.

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 Recommendations

Student skips key steps. Student does

not write out the entire procedure

-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

Student may show an understanding of key concepts in tutoring session but does not

perform well on classroom exams.

-Coordinate with the teacher to focus on high-impact tested

skills during tutoring.

-Allow students to problem-solve

independently and give sufficient time for self-correction to model the self-monitoring student

will need to perform during testing.

Poor Conversation or Academic Language SkillsWhat this looks like Recommendations

Student has difficulty understanding what the directions are asking the student to do and has difficulty understanding word problems.

Student does not use appropriate academic language and does not show an understanding of grade appropriate academic vocabulary when read.

-Listen to the student read the directions and problems.

-Dissect words to their mathematical root to help the student comprehend the mathematical meaning of the original word.

-Use vocabulary focused graphic organizers or pictures as visual tools to aid the student in thinking about mathematical language.

Poor English Language Skills

What this looks like Recommendations

Student is not able to read and understand

the text.

Student has difficulty understanding

academic language used in class. *Student

might be mathematically

proficient in another language.

-Read mathematical text with (or for) the student and discuss

meaning of academic words.

-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

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

Challenges students to perform calculations mentally

Online Worksheet Generators

Website Skills Problem Sets Number of Problems

The Math Worksheet Site

(very good for Fact Families practice)

http://themathworksheetsite.com

• Addition*• Subtraction*• Multiplication*• Division*• Mixed Facts≠

• Fractions±

• Graph Paper

*Single Digit (→ or ↓)Can specify #s used

*Multiple Digit*5 Minute Drill

≠Choose Operations±LCM & Reducing (choose difficulty and to

include Improper fractions)

Can choose length of problem set

90 problems

generated for 5 minute drill

Superkids – Math

http://www.superkids.com/aweb/tools/math

• +,-,×,÷, Mixed• Order of Ops• Fractions• Percents• Averages• Exponents

Control over:•Min value•Max value

•One number in all•Level of difficulty

Can choose length of problem set (Length varies

depending on concept)

Quick Tip Worksheets

Intervention Central(has literacy tools also!)

http://www.interventioncentral.org/index/php/tools/196-cbm-math-worksheet-generator

• Addition• Subtraction• Multiplication• Division• Mixed Facts

Less control over exact digits used More control over

EXACT type of problems (i.e. # digits in each term and regrouping)

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

6

, 12

, 12

Fractions

Addition

Division

Average

ADD all the terms together

and DIVIDE by the

number of terms there are.

Exponents

Bx Exponent

Base

24=2×2×2×2=16

Decimals & Percents

Decimals and Percents

D→P

Multiply by 100

P→D

Divide by 100

 

Math Games

• Who’s got 1

• Math Power Cards

• Rolling 100

• Add it Up

• Card Multiplication

• Variable Math War

• First to 100

• Ball Toss

• Prime Factor Relay

All of these games can be played before school, during T2 tutoring sessions, or during After School Homework Help

Math Power Cards

• 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.

1 2 3 4 5 6 7 8 9

Who’s Got 1?                 

• Skills: Adding fractions with unlike denominators • 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 ו 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.

100

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!