THIRD GRADE Session 1 Vacaville USD August 26, 2014

AGENDA Problem Solving and Patterns Math Practice Standards and Effective Questions Word Problems Counting, Place Value, Rounding Addition/Subtraction Strategies Daily Math/Math Talks Concept of Area Multiplication and Division

Expectations We are each responsible for our own learning and for the learning of the group. We respect each others learning styles and work together to make this time successful for everyone. We value the opinions and knowledge of all participants.

Regina’s Logo How many tiles are needed to make a Size 5? What about a Size 10? a Size 20? A Size 100?

Regina’s Logo What is a strategy that will let you quickly and easily figure out how many tiles you will need for any given size?

Regina’s Logo Recursive Add 3 each time SIZE # OF TILES 1 5 2 8 3 11 4 14 17

Regina’s Logo 3n + 2

Regina’s Logo 3n + 2

Regina’s Logo 2(n + 1) + n

Regina’s Logo 2n + (n + 2)

The Use of Effective Questions

Questioning plays a critical role in the way teachers Guide the class Engage students in the content Encourage participation Foster understanding

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

SMP’s So how does the use of effective questioning relate to the Standards for Mathematical Practice?

SMP’s and Questions Your group will receive 16 cards 8 lists of questions related to the SMP’s Your job is to match each SMP with the questions designed to support that SMP.

Asking Effective Questions Pick 2 colors... Use one color to highlight questions that you are already asking. Use the 2nd color to highlight questions that you would like to ask this year.

Additional Resources Effective Questions – PBS

Solving Word Problems

Read the entire problem, “visualizing” the problem conceptually Determine who and/or what the problem is about Rewrite the question in sentence form leaving a space for the answer.

Draw the unit bars that you’ll eventually adjust as you construct the visual image of the problem Chunk the problem, adjust the unit bars to reflect the information in the problem, and fill in the question mark.

Correctly compute and solve the problem (show all work!) Write the answer in the sentence and make sure the answer makes sense.

There are 83 girls and 76 boys in the third grade There are 83 girls and 76 boys in the third grade. How many total students are in the third grade? (Put Together/Take Apart – Total Unknown)

Tanya has 2 bags of apples Tanya has 2 bags of apples. If each bag has 3 apples, how many apples does she have? (Multiplication)

Patrick and Lilly start their chores at 5:00 p. m Patrick and Lilly start their chores at 5:00 p.m. Patrick finished at 5:31 and Lilly finished at 5:43. How much longer did it take Lilly to finish her chores? (Taken From – Result Unknown)

Caroline, Brian and Marta want to share a box of chocolates so that they each get the same amount. If there are 12 pieces in the box, how many will each child get? (Division – Fair Share)

Red, orange, and blue scarves are on sale for $4 each Red, orange, and blue scarves are on sale for $4 each. Nina buys 2 scarves of each color. How much does she spend altogether?

Standards 3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.3

Standards 3 This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

Standards 3 This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

Counting Place Value Rounding

Counting and Place Value How do we teach students to count “efficiently”?

Station Activity Count the number of objects Group by tens Groups 10 tens to make hundreds Locate number on number line If I count by 100, my number is closest to __ If I count by 10, my number is closest to __

Standards What are the place value standards for 3rd grade? What are students supposed to know and understand from 2nd grade?

Standards 3. NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100.

Standards What are the place value standards for 3rd grade? What are students supposed to know and understand from 2nd grade?

Supplemental Lessons Hide Zero Cards Other questions?

Addition and Subtraction

Standards What are the addition and subtraction standards for 3rd grade? What are students supposed to know and understand from 2nd grade?

Standards 3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Standards What are the addition and subtraction standards for 3rd grade? What are students supposed to know and understand from 2nd grade?

Progression Concrete Pictorial or Representational Abstract Invented and Alternative Algorithms Traditional Algorithms

Addition Strategies Solve 56 + 48 at your table using at least 3 different strategies.

Supplemental Lessons Unit 3 Lesson 1A Unit 3 Lesson 1B

Standards 3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Supplemental Lessons Unit 3 Lesson 3 – Word Problems Unit 3 Lesson 5 – Adding Larger Numbers (Regrouping Once) – Problem 1 Unit 3 Lesson 6 – Adding Larger Numbers (Regrouping Twice) – Problem 1 Unit 3 Lesson 9 – Number Lines

Subtraction Strategies Solve 96 – 47 at your table using at least 3 different strategies.

Math Talk

14 23 24 25 34

+6 24 30 64

The Concept of Area

What is Area? According to “Math is Fun”: Area is the size of a surface!

What is Area? Up to 3rd grade, students measurement experiences have focused primarily on linear measurements. So, how many lengths of 1” does it take to “fill” this rectangle?

What is Area? Area is the size of a surface! In order to consistently measure the size of a surface, length alone is not enough – we need a unit with both standard length and width – a unit square

AREA Using your color tiles, build a rectangle that has 3 rows with 4 tiles in each row. How many tiles did you use? How did you figure it out? (If you were a 3rd grade student)

Did I build a rectangle? How do you know? How many tiles did I use?

Find the area Find the area of each rectangle by filling each of the shapes with square tiles.

Finding Rectangles Count out 12 color tiles. Make as many different rectangles as you can that have an area of 12 square units.

Standards Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

Recognize area as an attribute of plane figures and understand concepts of area measurement. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

Relate area to the operations of multiplication and addition. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real-world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems.

Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems.

Supplemental Unit 1 Unit 1 Lesson 1 Unit 1 Lesson 2 Unit 1 Lesson 3

Multiplication and Division

In grade 3, instructional time should focus on four critical areas: developing understanding of multiplication and division and strategies for multiplication and division within 100; developing understanding of fractions, especially unit fractions (fractions with numerator 1); developing understanding of the structure of rectangular arrays and of area; describing and analyzing two-dimensional shapes.

In grade 3, instructional time should focus on four critical areas: developing understanding of multiplication and division and strategies for multiplication and division within 100; developing understanding of fractions, especially unit fractions (fractions with numerator 1); developing understanding of the structure of rectangular arrays and of area; describing and analyzing two-dimensional shapes.

In grade 3, instructional time should focus on four critical areas: developing understanding of multiplication and division and strategies for multiplication and division within 100; developing understanding of fractions, especially unit fractions (fractions with numerator 1); developing understanding of the structure of rectangular arrays and of area; describing and analyzing two-dimensional shapes.

Standards What are the multiplication and division standards for 3rd grade? What are students supposed to know and understand from 2nd grade?

Standards OA 1, 2, 3, 4, 5, 6, 7, (8, 9) NBT 3 MD 7

Multiplication Developing the concept of multiplication What strategies did we discuss last year for introducing multiplication?

Division Developing the concept of division What strategies did we discuss last year for introducing division?

Supplemental Unit Unit 4 Lessons 1-21

Sharing What strategies and activities did you try last year? What strategies and activities have you tried so far this year? What questions do you still have?