Transitioning to the Common Core State Standards – Mathematics 5 th Grade Session 3

1. Transitioning to the Common Core State Standards – Mathematics5th Grade Session 3 Pam Hutchison pam.ucdmp@gmail.com

2. AGENDA • Multi-Step and Other Word Problems • Review Math Practice Standards • Operations and Algebraic Thinking • Algebraic Expressions • Coordinate Graphing • Volume

3. Multi-Step Word Problems Baosaved $179 a month. He saved $145 less than Ada each month. How much would Ada save in three and a half years?

4. Multi-Step Word Problems The baker pays $0.80 per pound for sugar and $1.25 per pound for butter. How much the baker will spend if he buys 6 pounds of butter and 20 pounds of sugar?

5. Multi-Step Word Problems Ava is saving for a new computer that costs $1,218. She has already saved half of the money. Ava earns $14.00 per hour. How many hours must Ava work in order to save the rest of the money?

6. Multi-Step Word Problems A load of bricks is twice as heavy as a load of sticks. The total weight of 4 loads of bricks and 4 loads of sticks is 771 kilograms. What is the total weight of 1 load of bricks and 3 loads of sticks?

7. CCSS Mathematical Practices REASONING AND EXPLAINING 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others OVERARCHING HABITS OF MIND 1. Make sense of problems and perseveres in solving them 6. Attend to precision MODELING AND USING TOOLS 4. Model with mathematics 5. Use appropriate tools strategically SEEING STRUCTURE AND GENERALIZING 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

8. Math Practice Standards Using the MP descriptions from the 5thGrade Flipbook, describe how you are developing each of these practices in your students. • Be ready to share an example for each of the 8 Math Practices Standards. • Which standard is the hardest to implement?

9. Engage NY • Fluency Practice • Designed to promote automaticity of key concepts • Daily Math is another form of fluency practice • Application Problem • Designed to help students understand how to choose and apply the correct mathematics concept to solve real world problems • Read-Draw-Write (RDW): Read the problem, draw and label, write a number sentence, and write a word sentence

10. Engage NY • Concept Development • Major portion of instruction • Deliberate progression of material, from concrete to pictorial to abstract • Student Debrief • Students analyze the learning that occurred • Help them make connections between parts of the lesson, concepts, strategies, and tools on their own

11. OA.1 • Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

12. OA.2 • Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

13. Engage NY • Module 2 Lesson 3: Write and interpret numerical expressions and compare expressions using a visual model.

14. OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

15. G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

16. G.2 Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

17. Planning – Day 1 • Word Problem (embedded in opening activity) • Opening Activity • Number Lines • Locating Points Student Page

18. Day 1 y ___, ___ x y 2 3 _ 3_ 2_ 1 _ (2, 3)  x | | | | 0 1 2 3

19. Plotting Points • (4, 6) – Square • (3, 8) – Triangle • (7, 2) – Star • (5½, 7) – Circle • 6, 4½) – Heart • 3½, 2½) – Happy Face

20. Plotting Points • Practice Page1 • Practice Page 2

21. Day 2 • Review (TBD) • Opening Activity • Activity 1 • Draw an -axis so that it goes through points and , and label it -axis. • Draw the -axis so that it goes through points and , and label it -axis.

22. Day 2, cont. • Label 0 at the origin • On the -axis, we’re going to label the whole numbers only. The length of one square on the grid represents 1 fourth. How many whole numbers will be represented? • Count by fourths as we label the whole number grid lines. • What is the -coordinate of ? • What is the -coordinate of ?

23. Day 2, cont. • Label the -axisthe same way • Count by fourths as you label the whole number grid lines. • What is the -coordinate of ? • What is the -coordinate of ?

24. Day 2, cont. • Now let’s name the points • Put your finger on point A. We know the -coordinate is 1. What is the -coordinate? • So the point should be labeled (1, 0) • Do the same for point B. • Now put your finger on point C. We know the -coordinate is 2. What is the -coordinate? • How should the point be labeled? BE CAREFUL! • The point should be labeled (0, 2) • Do the same for point D.

25. Naming Points • Put your finger on point E • How do we find the -coordinate for point E ? • What is the -coordinate for point E ? • Write the -coordinate as part of a coordinate pair. • How do we find the -coordinate for point E ? • What is the -coordinate for point E ? • Write the -coordinate as part of a coordinate pair. • What are the coordinates for point E ? • Write that coordinate pair above point on your plane.

26. Naming and Locating Points • Find the coordinates for points F and G. • Name the point located at (1, 0). • Name the point located at (0, ). • Name the point whose distance from the -axis is . • Which point lies at a distance of from the -axis?

27. Naming and Locating Points • Plot a point at (3, 2 ). • What is the distance between and ? How did you find it? • Plot a point so that the - and -coordinates are both • Find the distance between and .

28. Naming and Locating Points • Coordinate Practice 2 page 1 • Coordinate Practice 2 page 2 • Engage NY Module 6 Topic A • Lessons 1, 2, and 3 • Lesson 4 – Battleship

29. Lesson 5

30. Lesson 6

31. Solving Problems • Module 6 Topic B • Hexagons in a Row • Module 6 Topic D • Patterns and Graphs 1

32. Volume • Module 5 • Topic A and Topic B