# MATHEMATICS TUTORING TIPS

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2 MATHEMATICS TUTORING TIPS Targeted Intervention: Practice and Strategies UTAH STATE OFFICE OF EDUCATION 250 East 500 South P.O. Box Salt Lake City, UT Larry K. Shumway, Ed.D. State Superintendent of Public Instruction Brenda Hales, M.Ed. Associate Superintendent Student Achievement and School Success Sydnee Dickson, Ed.D. Director of Teaching and Learning David Smith, M.Ed. Elementary Science and Math Coordinator Susan Okroy, M.Ed. Tutoring Specialist Copyright 2010, Utah State Office of Education

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5 Standard 4 Lesson 15 Add within 100, including adding a two-digit number and a one-digit number, and adding a two digit number and a multiple of Standard 5 Lesson 16 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. Standard 6 Lesson 17 Subtract multiples of 10 in the range from multiples of 10 in the range Domain: Measurement and Data Standard 1 Lesson 18 Order three objects by length; compare the lengths of two objects indirectly by using a third object. Standard 2 Lesson 19 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object end to end... Standard 3 Lesson 20 Tell and write time in hours and half-hours using analog and digital clocks Standard 4 Lesson 21 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. Domain: Geometry Standard 1 Lesson 22 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. Standard 2 Lesson 23 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quartercircles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders to create a composite shape, and compose new shapes from the composite shape. Standard 3 Lesson 24 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

7 5 Minutes 5 Minutes 8 3 = Check for understanding (work problem with student). As you tell the next story, the student will move the counters around the storyboard and give the subtraction number sentence at the end. Say, Five bears were sitting in the shade of the trees. (The student places 5 counters under the trees). All five bears decided to go for a swim. (The student should move the 5 counters to the lake.) How many bears are left sitting under the trees? (The student should say, Zero, because 5 5 = 0. ) GUIDED PRACTICE Monitor Student Work 7. Student works problems independently while tutor watches and coaches. Now the student will tell a subtraction story using the storyboard and counters, giving the correct subtraction sentence at the end. ASSESS Evaluate Student Demonstration 8. Student orally defines at least one Key Academic Mathematics Vocabulary word and skill or concept. Ask the student to explain what it means to subtract. The student should see subtraction as take away. 9. Student works a problem while explaining EVERY step orally. Using the storyboard, have the student tell a story and give an example of what he/she is doing. Example: Four dogs are playing under a tree. (The student puts 4 counters on the storyboard.) One dog decides that he has to go home. (The student removes one counter.) How many dogs are playing under the tree? (The student should be able to say, Three, because 4 1 = 3. )

8 Forest Storyboard

11 Forest Storyboard

16 5 Minutes 5 Minutes Tutor takes 5 cubes. Have the student count the 5 cubes so they understand that there are really 5 cubes. Place 1 cube in the cave and leave the remaining 4 on the table. Say to the student, I have 5 bears. I can see 4 cubes. So 5 subtract what gives me 4? I can figure how many by saying: 4 plus what will give me 5? I know that from counting on that I can count 4, then 5. So one bear is in the cave. So 5 1 is 4 because equals Check for understanding (work problem with student). The tutor will observe the student performing the task. The student must be able to tell how many bears are in the cave and give the number sentences to explain. The tutor will prompt the student as needed. GUIDED PRACTICE Monitor Student Work 7. Student works problems independently while tutor watches and coaches. The student will be able to tell the tutor the number of bears in the cave while playing the game using different combinations of bears in and out of the cave. ASSESS Evaluate Student Demonstration 8. Student orally defines at least one Key Academic Mathematics Vocabulary word and skill or concept. Puts some cubes on the table and some in one hand. Ask, What is a way that we can figure out how many bears are in the cave? (Count on.) 9. Student works a problem while explaining EVERY step orally. Take the cubes and put some on the table and some in one hand, making sure the student knows how many cubes are altogether. Have the student orally tell how many bears are outside and then correctly figure how many are on the inside.

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20 Number Line

22 5 Minutes 5 Minutes ten! Set the cards aside. 6. Check for understanding (work problem with student). After the student has found the various combinations, mix those cards and put down some other cards. Ask the student to find two cards that will make a sum of 10. GUIDED PRACTICE Monitor Student Work 7. Student works problems independently while tutor watches and coaches. Tutor and student both receive 5 cards, leaving the other cards in a pile between them. Do not show the other player your cards. First player will look at the cards in his/her hand to see if he/she has one way to make ten using two cards. If he/she does, he/she will lay down the pair of cards, then draw two more cards from the pile. Second player will do the same. If a player does not have a pair of cards to make ten, he/she loses a turn and will draw another card on his/her next turn. Play will continue until there are no more ways to make ten. The player with the most ways to make ten is the winner. ASSESS Evaluate Student Demonstration 8. Student orally defines at least one Key Academic Mathematics Vocabulary word and skill or concept. Give the student a number between 0 and 9 and ask what he/she would need to add to it in order to make ten (e.g., if you give the number 4, the student should tell you he/she needs 6 more to make 10). Ask, What does it mean to make ten? 9. Student works a problem while explaining EVERY step orally. Have the cards 0 9 out on the table so the student can see the numbers. Give the student a card with the number 6. Ask him/her to pick the card that would be needed to make ten. (4) Ask the student why he/she chose that card.

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26 5 Minutes 5 Minutes Turn over another card and place it on the box that reads 2 nd Card. If either card is a number sentence, add the numbers together then determine whether the equation is true or false (e.g., if the 1 st card says 6 and the 2 nd says 2 + 7, the equation is false because 6 is not equal to [the same as] 9, but if the 1 st card says 6 and the 2 nd says 5 + 1, the equation is true because 6 is equal to [the same as] 6). 6. Check for understanding (work problem with student). Using the cards, have the student work one round of the game, placing the cards correctly and telling whether the equation is true or false. GUIDED PRACTICE Monitor Student Work 7. Student works problems independently while tutor watches and coaches. Repeat the steps beginning with step 4. This time the student will work independently to put the cards on the mat, add numbers together if necessary, and determine whether the equation is true or false. If the equation is true, the student may keep the cards. If it is false, the student will return the cards to the table. The student will continue until time is up. ASSESS Evaluate Student Demonstration 8. Student orally defines at least one Key Academic Mathematics Vocabulary word and skill or concept. Ask the student to explain what equal means. Ask the student to define true and false. 9. Student works a problem while explaining EVERY step orally. Using the cards, have the students work one round of the game placing the cards correctly and telling whether the equation is true or false. Have him/her explain why he/she placed each card where he/she did, and how he/she knew whether the equation was true or false.

27 Equals Mat 1 st Card 2 nd Card

29 5 Minutes 7. Student works problems independently while tutor watches and coaches. The student will repeat the steps from step 6 with little or no help. Continue until time is up. ASSESS Evaluate Student Demonstration 8. Student orally defines at least one Key Academic Vocabulary word and skill or concept. Ask the student to explain or demonstrate what it means to count on. He/she should be able to tell you that it means to start with a number and then count on the other number to find the sum. 9. Student works a problem while explaining EVERY step orally. The student is given a numeral card, then a dot card. The student must be able to say the numeral and then count the number of dots aloud and give the sum of the problem.

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32 Lesson 9 to be inserted when completed.

34 5 Minutes ASSESS Evaluate Student Demonstration 8. Student orally defines at least one Key Academic Vocabulary word and skill or concept. When game is completed, the tutor draws two cards and makes a two-digit number. The tutor then asks, Which digit is in the tens place? How many tens are in that number? Which digit is in the ones place? How many ones are in that number? 9. Student works a problem while explaining EVERY step orally. The tutor shuffles the cards when the game is finished. The student draws two cards and places them on the table as a two-digit number. The student reads the number, builds the number, and tells the number of tens and ones.

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38 tens ones I have tens and ones. I have total.

39 8 Minutes 2 Minutes Before You Begin Utah State Office of Education FIRST GRADE Lesson 11 Mathematics Tutoring Session Template Common Core Identification Domain: Number and Operations in Base Ten Cluster: Understand place value. Standard 2: Understand that the two digits of a two-digit number represent amounts of tens and ones. 2a: Ten can be thought of as a bundle of ten ones, called a ten. Key Academic Mathematics Vocabulary (3 or Fewer) Ten(s) A group/groups of ten ones. Notes and Materials Notes and suggestions for an effective lesson: Use correct vocabulary, calling ten ones a ten and several groups of ten tens. Materials you will need: 50 single objects per player (e.g., Popsicle sticks, straws, toothpicks) Number cube with numbers cups per player LAUNCH Assess and Provide Background Knowledge 1. Connect to prior learning. Use a "hook" to gain the student's attention. Say, Let s count to 10 together. Ask the student to show ten objects. 2. Introduce and review Key Academic Mathematics Vocabulary. Ten(s) A group/ groups of ten ones. INSTRUCT Provide Explicit, Interactive Instruction 3. State the objective. Student will be able to make bundles of ten. 4/5. Provide explicit, step-by-step instructions and model. Model making a group of ten and have the student do the same. Both student and tutor will be given 5 cups and 50 objects for counting. Roll the number cube and pull out objects to match the number shown on the cube (e.g., if a 5 is rolled, put down 5 Popsicle sticks). The student will do the same, with any help necessary from the tutor. Play will continue in the same manner. Once either student or tutor reaches ten objects, he/she will bundle them and place them in one of the cups. If there are leftover objects after making the bundle of ten, leave them out and continue adding to them as the game progresses. Emphasize that the objects in the cup now represent a ten. The next time a group of ten objects has been collected, they will be bundled and placed in a different cup. Have the student say the total number of objects he/she now has. After the tutor and student have each rolled the number cube 8 times, the player with more bundles of ten is the winner. Have the student count by tens and ones to state the number of objects each player has at the end of game. 6. Check for understanding (work problem with student). Watch as the student counts the objects and then makes a bundle when he/she has collected 10 objects.

40 5 Minutes 5 Minutes GUIDED PRACTICE Monitor Student Work 7. Student works problems independently while tutor watches and coaches. Play the game again, this time allowing the student to work more independently on determining when to bundle the objects. ASSESS Evaluate Student Demonstration 8. Student orally defines at least one Key Academic Vocabulary word and skill or concept. Ask the student to explain what a ten is and where tens come from. 9. Student works a problem while explaining EVERY step orally. The student will roll the number cube and take objects to match the number cube. He/she will continue rolling and making bundles until he/she has 2 bundles. When the student reaches the ten and bundles, he/she orally explains why he/she bundles the objects. After that, one bundle is made and the number cube is rolled. The student will also explain when he/s can t make a bundle.

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42 8 Minutes 2 Minutes Before You Begin Utah State Office of Education FIRST GRADE Lesson 12 Mathematics Tutoring Session Template Common Core Identification Domain: Number and Operations in Base Ten Cluster: Understand place value. Standard 2: Understand that the two digits of a two-digit number represent amounts of tens and ones. 2b: The numbers from 11 to 19 are composed of a ten and 1, 2, 3, 4, 5, 6, 7, 8, or 9 ones. Key Academic Mathematics Vocabulary (3 or Fewer) Ten(s) A group/groups of ten ones. One(s) A single unit that cannot be grouped into a ten. Notes and Materials Notes and suggestions for an effective lesson: Use correct vocabulary, calling single objects ones, ten ones a ten, and several groups of ten tens. Materials you will need: Number cube with numbers unifix cubes per player Place Value Mat LAUNCH Assess and Provide Background Knowledge 1. Connect to prior learning. Use a "hook" to gain the student's attention. Say, Let s count to one hundred by tens! 2. Introduce and review Key Academic Mathematics Vocabulary. Place one unifix cube on the table and say one. Put another unifix cube on the table and say two. Continue until there are ten unifix cubes on the table. Then snap them together, show that there is now a bundle that has ten ones, and tell the students that now you have a ten. Continue putting single unifix cubes on the table and saying the number until you can make another bundle. Show the student that there are now two bundles of ten. INSTRUCT Provide Explicit, Interactive Instruction 3. State the objective. The student will be able to identify numbers in terms of tens and ones. 4/5. Provide explicit, step-by-step instructions and model. Demonstrate vocabulary, and model building the numbers Have the Place Value Mat on the table; roll the number cube and place that number of unifix cubes in the ones column on the mat. Say the sentence at the bottom of the mat using the correct numbers (e.g., I have 0 tens and 5 ones. I have 5 ). Roll the number cube again, adding the corresponding number of unifix cubes onto the ones column on the mat. Ask the student to help count the ones. If there are10 or more unifix cubes, ask the student what he/she thinks should be done. Guide the student toward the correct answer (to put 10 of the cubes in the tens column). Repeat the sentence at the bottom of the mat using the new numbers (e.g., I have 1 ten and 2 ones. I have 12 ). Once the number 20 is reached, the game is over. 6. Check for understanding (work problem with student). Watch the student as he/she builds the numbers and places them in the correct column on the place value mat and say the amount correctly in the number of tens and ones.

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DRAFT MATHEMATICS TUTORING TIPS Targeted Intervention: Practice and Strategies UTAH STATE OFFICE OF EDUCATION 250 East 500 South P.O. Box 144200 Salt Lake City, UT 84114-4200 Larry K. Shumway, Ed.D. State

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