Presentation Transcript

1. 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
2. CITY YEAR CHICAGO CITY YEAR CHICAGO CITY YEAR CHICAGO Math 202 Session Developer: Mari Mermelstein City Year Chicago
3. 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
4. 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 Math Anxiety
5. Weak Computational Skills
6. Weak Conceptual Understanding
7. Low Work Completion Rate
8. Lack of Confidence
9. Unable/Unwilling to Write Out Complete Solutions
10. Poor Test-Taking Skills
11. Poor Conversation or Academic Language Skills
12. Poor English Language Skills
13. Math Tutoring
14. 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!!!!
15. 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
16. Online Worksheet Generators
17. Fact Families
18. Order of Operations
19. Order of Operations
20. Leave-Change-Opposite (LCO) Apply when subtracting numbers it turns subtraction problems into addition problems
21. 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 _____________
22. Fractions - Reducing
23. Fractions – Least Common Multiple
24. Fractions – Common Denominators 4 , 8 , 12 , 12 6
25. Fractions Addition Division
26. Average ADD all the terms together and DIVIDE by the number of terms there are.
27. Exponents Bx Exponent Base 24=2×2×2×2=16
28. Decimals & Percents Decimals and Percents D→P Multiply by 100 P→D Divide by 100
29. 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
30. Math Power Cards 2 3 5 6 7 8 1 4 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.
31. 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)
32. 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
33. 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.
34. First to 100 100 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.
35. 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.
36. 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.
37. Example Leader rolled a 2 and a 5, so the multiplier for this round is 7.
38. 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.
39. Example z = 2x + 3y. y x
40. 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!