Vacaville USD November 3, 2014

AGENDA Problem Solving and Patterns Math Practice Standards and High Leverage Instructional Practices Number Talks –Computation Strategies Word Problems –Number Lines –Elapsed Time Multiplication

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.

Cubes in a Line How many face units can you see when cubes are put together?

Cubes in a Row How many face units do you see on 1 cube?

Cubes in a Row How many face units do you see on 2 cubes? How can you keep track of what sides you have counted?

Cubes in a Row You are going to be given 2 strips of paper like this: _____________ number of cubes number of face units 7

Cubes in a Row What patterns do you see? How could those patterns help you figure out how many face units there would be?

Math Practice Standards Remember the 8 Standards for Mathematical Practice Which of those standards would be addressed by using a problem such as this?

CCSS Mathematical Practices OVERARCHING HABITS OF MIND 1.Make sense of problems and persevere in solving them 6.Attend to precision REASONING AND EXPLAINING 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 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

High Leverage Instructional Practices

High-Leverage Mathematics Instructional Practices An instructional emphasis that approaches mathematics learning as problem solving. 1.Make sense of problems and persevere in solving them.

An instructional emphasis on cognitively demanding conceptual tasks that encourages all students to remain engaged in the task without watering down the expectation level (maintaining cognitive demand) 1.Make sense of problems and persevere in solving them.

Instruction that places the highest value on student understanding 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively

Instruction that emphasizes the discussion of alternative strategies 3.Construct viable arguments and critique the reasoning of others

Instruction that includes extensive mathematics discussion (math talk) generated through effective teacher questioning 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 6.Attend to precision 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

Teacher and student explanations to support strategies and conjectures 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others

The use of multiple representations 1.Make sense of problems and persevere in solving them. 4.Model with mathematics 5.Use appropriate tools strategically

Number Talks

What is a Number Talk? Also called Math Talks A strategy for helping students develop a deeper understanding of mathematics –Learn to reason quantitatively –Develop number sense –Check for reasonableness –Number Talks by Sherry Parrish

What is Number Talk? A pivotal vehicle for developing efficient, flexible, and accurate computation strategies that build upon key foundational ideas of mathematics such as –Composition and decomposition of numbers –Our system of tens –The application of properties

Key Components Classroom environment/community Classroom discussions Teacher’s role Mental math Purposeful computation problems

Classroom Discussions What are the benefits of sharing and discussing computation strategies?

Students have the opportunity to: –Clarify their own thinking –Consider and test other strategies to see if they are mathematically logical –Investigate and apply mathematical relationships –Build a repertoire of efficient strategies –Make decisions about choosing efficient strategies for specific problems

5 Goals for Math Classrooms Number sense Place Value Fluency Properties Connecting mathematical ideas

Clip 3.2 – 3 rd Grade Addition: Before we watch the clip, talk at your tables –What possible student strategies might you see? –How might you record them?

How do the student strategies demonstrate number sense? What evidence is there that the students understand place value? What examples of properties can be observed in the strategies/discussions? How does the teacher connect math ideas throughout the talk?

Clip 3.4 – 3 rd Grade Subtraction: 70 – 34 Before we watch the clip, talk at your tables –What possible student strategies might you see? –How might you record them?

Do you see evidence of students demonstrating: Number sense Place Value Fluency Properties Connecting mathematical ideas

Solving Word Problems

3 Benefits of Real Life Contents Engages students in mathematics that is relevant to them Attaches meaning to numbers Helps students access the mathematics.

Mr. Alvarez drove 233 miles to get 500 baseballs on Monday. On Friday Mr. Alvarez drove 987 miles. How many total miles did Mr. Alvarez drive?

There were 333 children in a spelling contest. Of those, 219 were girls. How many more girls than boys were in the spelling contest?

Three friends go apple picking. They pick 13 apples on Saturday and 14 apples on Sunday. They share the apples equally. How many apples does each person get?

Jason earns $6 per week for doing all his chores. On the fifth week he forgets to take out the trash so he only earns $4. How much did Jason earn in 5 weeks?

Using an Open Number Line

A cricket jumped 7 centimeters forward and 12 centimeters back then stopped. If the cricket started at 27 on the ruler, where did the cricket stop?

James and Chloe each have pet snakes. James’ snake is 35 centimeters long. Chloe's snake is 7 centimeters longer than James’. How long is Chloe's snake?

Bill throws his baseball 41 feet, which was 14 feet farther than Samantha threw her baseball. How far did Samantha throw her baseball?

Mei’s frog leaped forward 34 centimeters. Then it leaped forward some more. In all, it leaped 61 centimeters. How far did Mei’s frog leap the second time?

Halle has two ribbons. The blue ribbon is 58 cm long. The green ribbon is 83 cm long. How much longer is the green ribbon?

Elapsed Time

We started math at 10:15 a.m. We worked for 23 minutes. What time was it when we ended?

The soccer game started at 11:45 and lasted 52 minutes. What time did it end?

Leslie starts reading at 11:24 a.m. She finishes reading at 11:57 a.m. How many minutes does she read?

The school ballet recital begins at 12:17 p.m. and ends at 12:45 p.m. How many minutes long is the ballet recital?

Joe finished his homework at 5:48 p.m. He worked for 32 minutes. What time did he start his homework?

It took me 42 minutes to cook dinner last night. I finished cooking at 5:56 p.m. What time did I start?

It takes Austin 4 minutes to take out the garbage, 12 minutes to wash the dishes, and 13 minutes to mop the kitchen floor. Austin’s bus arrives at 7:55 a.m. If he starts his chores at 7:30 a.m., will he be done in time to meet his bus?

Multiplication and Division FACTS

Number Talk 3.5: 7 x 7 How do students strategies demonstrate: –an understanding of multiplication? –number sense? How does fluency with small numbers support student strategies? How does the teacher connect math ideas throughout the number talk? How could the strategies be connected using an array?

Number Talk 3.6

Multiplication and Division Strategies Repeated Addition/Subtraction Skip Counting Equal Groups Arrays and Area Models Partial Products/Partial Quotients Traditional US Algorithm

Templates Multiplication – Division Template 1 6 x 8 =

Templates Multiplication – Division Template 2 42  7 =

Area

Informal Area

Formal Area 3 in 7 in 8 in 6 in 21 sq in 48 sq in

Area vs Perimeter Purposely connected area and multiplication Purposely separated area and perimeter