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**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

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**CITY YEAR CHICAGO CITY YEAR CHICAGO**

Math 202 Session Developer: Mari Mermelstein City Year Chicago 2

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**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

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**Math Anxiety Weak Conceptual Understanding Weak Computational Skills**

Poor test-taking skills Low Work Completion Rate Poor English Language Skills Weak Computational Skills Poor conversation or academic language skills Lack of Confidence Unable/Unwilling to write out complete solutions

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**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.

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**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.

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**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.

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**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

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**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.

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**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.

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**Poor Conversation or Academic Language Skills**

What 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.

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**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.

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Math Tutoring

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**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!!!!

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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

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**Online Worksheet Generators**

Website Skills Problem Sets Number of Problems The Math Worksheet Site (very good for Fact Families practice) 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 +,-,×,÷, 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!) 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) Answer sheet automatically created

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Fact Families

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Order of Operations

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Order of Operations

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**Leave-Change-Opposite (LCO)**

Apply when subtracting numbers it turns subtraction problems into addition problems

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**Multiplying and Dividing with Positive and Negative Numbers**

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 _____________

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Fractions - Reducing

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**Fractions – Least Common Multiple**

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**Fractions – Common Denominators**

4 , 8 , 12 6 , 12

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Fractions Addition Division

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Average ADD all the terms together and DIVIDE by the number of terms there are.

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Exponents Bx Exponent Base 24=2×2×2×2=16

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**Decimals & Percents Decimals and Percents D→P Multiply by 100 P→D**

Decimals and Percents D→P Multiply by 100 P→D Divide by 100

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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 Math Power Cards Rolling 100 Add it Up Card Multiplication Variable Math War First to 100 Ball Toss Prime Factor Relay

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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.

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**Who’s Got 1? Skills: Adding fractions with unlike denominators**

Skills: Adding fractions with unlike denominators Set Up: 9 index cards labeled 1 6 , , 1 4 , , 1 3 , 3 8 , , , and 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)

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**Add It Up Skills: Addition with 1-4 digit numbers**

Set Up: Paper and pencil 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

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**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.

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**100 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.

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**Rolling 100 Skills: Addition with 2 digit numbers**

Set Up: Two dice per group, pencil and paper 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.

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**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.

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Example Leader rolled a 2 and a 5, so the multiplier for this round is 7.

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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.

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Example z = 2x + 3y. x y

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**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!

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