Day 2 – Supporting Derived Facts with Number Talks Goals: I can use ten-­‐frames and rekenreks to carry out number talks with my students. I can help my students compose and decompose numbers. I can describe several strategies that children use to derive addition facts. I can describe the pre-­‐requisite strategies that children need to use a “make ten” strategy when adding whole numbers. Minnesota Standards Use objects and pictures to represent situations involving combining and separating. K.1.2.1 Use objects and draw pictures to find the sums and differences of numbers between 0 and 10. K.1.2.2 Compose and decompose numbers up to 10 with objects and pictures. Use a variety of models and strategies to solve addition and subtraction problems in real-­‐world and mathematical contexts. 1.1.2.1 Use words, pictures, objects, length-­‐based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-­‐part-­‐total, adding to, taking away from and comparing situations. 1.1.2.2 Compose and decompose numbers up to 12 with an emphasis on making ten. Use number sentences involving addition and subtraction basic facts to represent and solve real-­‐
world and mathematical problems; create real-­‐world situations corresponding to number sentences. 1.2.2.1 Represent real-­‐world situations involving addition and subtraction basic facts, using objects and number sentences. 1.2.2.2 Determine if equations involving addition and subtraction are true. Demonstrate mastery of addition and subtraction basic facts; add and subtract one-­‐ and two-­‐digit numbers in real-­‐world and mathematical problems. 2.1.2.1 Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtraction to generate basic facts. 2.1.2.2 Demonstrate fluency with basic addition facts and related subtraction facts. Use number sentences involving addition, subtraction and unknowns to represent and solve real-­‐
world and mathematical problems; create real-­‐world situations corresponding to number sentences. 2.2.2.1 Understand how to interpret number sentences involving addition, subtraction and unknowns represented by letters. Use objects and number lines and create real-­‐world situations to represent number sentences. 2.2.2.2 Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Visualizing Numbers – Prove it! figure number sentence I. II. III. IV. V. Day 2 – Supporting Derived Facts page 2 Problem Type: How many children are in the class? There are 7 boys and 8 girls in Ms. Weil’s class. Question: a) Direct Modeling b) Counting On c) Derived Facts (Number Sense)/ Recall Day 2 – Supporting Derived Facts page 3 Problem Type: Monica has 7 carrots. Abdi gives her some more carrots, now Monica has 13 carrots. Question: a) Direct Modeling b) Counting c) Derived Facts (Number Sense)/ Recall Day 2 – Supporting Derived Facts page 4 Problem Type: Separate (result unknown) Write a separate (result unknown) for the number sentence 14 − 8 =? a) Direct Modeling b) Counting c) Derived Facts (Number Sense)/ Recall Day 2 – Supporting Derived Facts page 5 Composing and Decomposing Numbers Part 1: Move from Counting Rekenrek: Start with 5 on top. “How many more to get to 8? Show how you did it.” Rekenrek: Show 5 on top. “How many more to get to 9?” Show how you did it.” Part 2: Composing Numbers -­‐ 7 Ask: “How many beads do you see? How do you see them?” A. 5 on top 0 on the bottom B. 5 on top 2 on the bottom C. D. 4 on top 3 on the bottom 2 on top 5 on the bottom Part 3: Composing 9 Ask: “How many beads do you see? How do you see them?” A. 4 on top 5 on the bottom B. 3 on top 6 on the bottom C. D. 2 on top 7 on the bottom 1 on top 8 on the bottom Day 2 – Supporting Derived Facts page 6 Watching a Number Talk (Grade K – Video K.2 – 5 minutes 8 seconds) Discussion Questions 1. How does the rekenrek warm-­‐up with four and six provide the teacher with information to guide her instructional decisions? 2. When does the teacher tell or show information to students and when does she provide opportunities for them to make sense of the mathematics? How is this similar to or different than your math instruction? 3. Are there number combinations that seem more accessible to the students? How does the teacher build on this foundation? Day 2 – Supporting Derived Facts page 7 Key Components of a Number Talk Four Procedures and Expectations Essential to Number Talks (from Number Talks by Sherry Parrish) 1. Select a designated location that allows you to maintain close proximity to your students for informal observations and interactions. 2. Provide appropriate wait time for the majority of students to access the problem. 3. Accept, respect, and consider all answers. 4. Encourage student communication throughout the number talk. Practice Rekenrek Talks – Groups of 4 Day 2 – Supporting Derived Facts page 8 Ten-­‐Frames Day 2 – Supporting Derived Facts page 9 Number Talks with Ten-­‐Frames Kindergarten – Single Ten-­‐Frames “How many dots do you see? How do you see them?” A. B. C. First Grade – Making Tens using Double Ten-­‐Frames “How many dots do you see? How do you see them?” A. B. C. Day 2 – Supporting Derived Facts page 10 Second Grade – Making Tens using Number Sentences “What is the sum? How did you get your answer?” 8 + 2 8 + 5 8 + 4 8 + 7 Second Grade – Looking for Landmark or Friendly Numbers using Number Sentences “What is the sum? How did you get your answer?” 40 + 4 39 + 4 39 + 15 39 + 39 Day 2 – Supporting Derived Facts page 11 Composing and Decomposing Numbers Part 1: Move from Counting Ten-­‐Frame: Start with 5 on top. “How many more to get to 8? Show how you did it.” Ten-­‐Frame: Show 5 on top. “How many more to get to 9?” Show how you did it.” Part 2: Composing Numbers -­‐ 7 Ask: “How many dots do you see? How do you see them?” A. 5 on top 0 on the bottom B. 5 on top 2 on the bottom C. D. 4 on top 3 on the bottom 2 on top 5 on the bottom Part 3: Composing 6 Ask: “How many dots do you see? How do you see them?” A. 4 on top 2 on the bottom B. 3 on top 3 on the bottom C. D. 2 on top 4 on the bottom 5 on top 1 on the bottom Day 2 – Supporting Derived Facts page 12 Planning a Number Talk (5 minutes) Select a Critical Learning Phase (pages 43-­‐71): Picture Key Teacher Questions Predicted number sentences Day 2 – Supporting Derived Facts page 13 Adding Numbers Watching a Math Talk (Grade 2 – Video 2.1 – 4 minutes 40 seconds) Write equations that match student thinking. Day 2 – Supporting Derived Facts page 14 Practicing a Math Talk Grade K – Doubles Grade 1 – Doubles and near doubles Grade 2 – Adding 8 plus another number Day 2 – Supporting Derived Facts page 15 “Make-­‐a-­‐ten” for Addition There are three prerequisites for children to use the make-­‐a-­‐ten strategy effectively (From Fuson Ch. 6 in Research Companion page 74): 1) They must know what number makes a ten with each number up to 10 (e.g. 10=9+1, 8+2, 6+4 or 7+3) 2) Be able to break a number apart into any of its two addends (e.g. 8 = 5+3 so that when they do 8 + 7 they can then do 5+3+7 = 5+10 = 15) 3) They need to know that 10 + n = 1n (e.g. 10 + 7 = 17) Using Open Number Sentences to Make Ten Day 2 – Supporting Derived Facts page 16