First Grade CCSS–M, and Daily Math Vacaville USD September 6, 2013

AGENDA The CCSS-M: Math Practice Standards Daily Math Programs Subitizing Number of the Day Word Problems Model Drawing (steps) And other areas Addition and Subtraction Facts Exploring Resources Report Cards and Assessments

The Common Core State Standards – Mathematics

CCSS – M The CCSS in Mathematics have two sections: Standards for Mathematical CONTENT and Standards for Mathematical PRACTICE know The Standards for Mathematical Content are what students should know. do The Standards for Mathematical Practice are what students should do.  Mathematical “Habits of Mind”

Standards for Mathematical Practice

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

Reflection How are these practices similar to what you are already doing when you teach? How are they different? What concerns do you have with regards to the Standards for Mathematical Practice?

Standards for Mathematical Content

Are a balanced combination of procedure and understanding. Stress conceptual understanding of key concepts and ideas

Standards for Mathematical Content Continually return to organizing structures to structure ideas place value properties of operations These supply the basis for procedures and algorithms for base 10 and lead into procedures for fractions and algebra

“Understand” means that students can… Explain the concept with mathematical reasoning, including  Concrete illustrations  Mathematical representations  Example applications

Organization K-8 Domains  Larger groups of related standards. Standards from different domains may be closely related.

Domains K-5 Counting and Cardinality (Kindergarten only) Operations and Algebraic Thinking Number and Operations in Base Ten Number and Operations-Fractions (Starts in 3 rd Grade) Measurement and Data Geometry

Organization K-8 Clusters  Groups of related standards. Standards from different clusters may be closely related. Standards  Defines what students should understand and be able to do.  Numbered

A Daily Math Program

5 Big Ideas 1. From Kindergarten on, help children develop flexible ways of thinking about numbers by having them “break apart” numbers in multiple ways

5 Big Ideas 2.From their earliest days in school, children should regularly solve addition, subtraction, multiplication, and division problems.

5 Big Ideas 3. Problem solving of all types should be a central focus of instruction.

5 Big Ideas 4.Develop number sense and computational strategies by building on children’s ideas and insights.

5 Big Ideas 5.Teach place value and multi-digit computation throughout the year rather than as “chapters”.

Number Sense What is “number sense”? The ability to determine the number of objects in a small collection, to count, and to perform simple addition and subtraction, without instruction.

Visualize Numbers I am going to show you a slide for a few seconds Record the number of dots in Box A and in Box B READY?

Box A Box B

Record your answers  Box A  Box B 

Share On a scale of 1-5, how confident are you that your answer is correct?

SUBITIZING Ability to recognize the number of objects in a collection, without counting When the number exceeds this ability, counting becomes necessary

Box A Box B

Perceptual Subitizing Maximum of 5 objects Helps children  Separate collections of objects into single units  Connect each unit with only one number word  Develops the process of counting

Subitizing Let’s try again. Ready??

Box C Box D

Record your answers  Box C  Box D 

Share On a scale of 1-5, how confident are you that your answer is correct?

Box C Box D

Box C Box D

Conceptual Subitizing Allows children to know the number of a collection by recognizing a familiar pattern or arrangement Helps young children develop skills needed for counting Helps develop sense of number and quantity

Children who cannot conceptually subitize will have problems learning basic arithmetic processes

Renee – Modeling Daily Math Subitizing

Practicing Subitizing Use cards or objects with dot patterns Groups should stand alone Simple forms like circles or squares Emphasize regular arrangements that include symmetry as well as random arrangements Have strong contrast with background Avoid elaborate manipulatives

How Many Dots?

What’s My Number

What’s 1 more than

What’s 1 less than

Ten Frames and Dot Patterns

Ten Frames  

   

    

Ten Sticks

Base 10 Shorthand

Kindergarten – OA 4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

Tens Facts   = 10

Tens Facts   = 10

Tens Facts   = 10

Kindergarten – OA 3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = and 5 = 4 + 1).

Part-Whole Relations

44444 Number Bonds

Number Bonds – 17 17

Number Bonds – 43 43

Renee – Modeling Daily Math Number of the Day of School Number of the Day on the Calendar Random Number of the Day

Number of the Day Number of the Day of School Counting  Ones  Tens  Counting On Counting back

Number of the Day Place Value  Straws  Ten Frames  Ten Sticks  Hundred’s Chart Computation

Number of the Day Today is the 16 th day of school  Put in one more straw. How many ones do we have? Do we need to make another bundle?  Count the number of ten’s bundles – 1  So, how many tens to make 16?  How many ones?  Let’s count the number of the day by counting tens and counting on the ones – 10, 11, 12, 13, 14, 15, 16

Number of the Day Today is the 16 th day of school  What is 1 more than 16?  What is one less than 16?  What if I put in another bundle of 10? Now what would the number be?  What if I took out a bundle of 10? What would the new number be?  Find at least 5 possible number bonds (using 2 numbers) that you can make with 16.

Number of the Day Today is the 78 th day of school  Put in one more straw. How many ones do we have? Do we need to make another bundle?  Count the number of ten’s bundles  Let’s count the number of the day by counting tens and counting on the ones – 10, 20, 30, 40, 50, 60, 70, 71, 72, 73, 74, 75, 76, 77, 78  How many ten’s in 78?  How many ones in 78?

Number of the Day Today is the 78 th day of school  Write 78 in expanded form.  What is 1 more than 78? 1 less?  What is 10 more than 78? 10 less?  Find at least 3 number sentences for 78.  Use at least 3 numbers  Use at least 2 different operations

Number of the Day Number of Day on Calendar Rote Counting Calendar Questions – Days of the week, months of the year, tomorrow and yesterday, how many Saturday’s have we had, looking at the columns of the calendar, etc.)

Number of the Day Number of Day on Calendar Addition Problems Number Bonds 1 more 1 less, 10 more 10 less Predicting

Daily Math, continued Patterns Predict the next element in the pattern (shape, numeric, location, etc.) Identifying the repeating part

Random Number of the Day The number of the day is: 36  Who can read the number?  What digit is in the ten’s place? The one’s place?  Write the number in expanded form.  What is 1 more than 36? 1 less?  What is 10 more than 36? 10 less?  Find at least 3 number sentences for 36.

Random Number of the Day II Popsicle sticks to generate random number of the day 5 tens, 9 ones  What is the number?  Etc. 3 ones, 7 tens  What is the number?  Etc.

My Number of the Day Is my number larger or smaller than your number?  How do you know?  Fill the number in so that each makes a true statement: ___ Write a number that is larger than the number of the day. Write a number that is smaller than the number of the day.

CCSS - NBT Extend the counting sequence. 1.Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

CCSS - NBT Understand place value. 2.Understand that the two digits of a two- digit number represent amounts of tens and ones. Understand the following as special cases: a)10 can be thought of as a bundle of ten ones — called a “ten.” b)The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

CCSS - NBT Understand place value. c)The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). 3.Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

CCSS – NBT Use place value understanding and properties of operations to add and subtract. 5.Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

Math Talk Students do better in classrooms where teachers use numbers as regular part of day

Reflection Where, in the course of a normal day, can you find places to talk about numbers OUTSIDE OF MATH TIME? Where do numbers occur in the everyday lives of your students?

Daily Math, continued Word Problems All four operations ( +, -, x, ÷) Clear action problems verses passive problems All problem types appropriate to grade level (see chart)

Model Drawing Steps 1.Read the entire problem, “visualizing” the problem conceptually 2.Decide and write down (label) who and/or what the problem is about 3.Rewrite the question in sentence form leaving a space for the answer. 4.Draw unit bars of equal length that you’ll eventually adjust as you construct the visual image of the problem

Model Drawing Steps 5.Chunk the problem and adjust the unit bars to reflect the information in the problem 6.Determine exactly “what” you’re being asked to find and place a question mark in the place on the model drawing that reflects the “what”

Model Drawing Steps 7.Compute the problem to come up with an answer (show all work!) 8.Write the answer in a complete sentence that clearly states the solution

Pre-Model Drawing Steps 1.Read the entire problem, “visualizing” the problem conceptually 2.Decide and write down (label) who and/or what the problem is about 3.Rewrite the question in sentence form leaving a space for the answer.

Pre-Model Drawing Steps 4.Chunk the problem to determine what you know, what the action is, and what you are being asked to find 5.Compute the problem to come up with an answer (show all work!) 6.Write the answer in a complete sentence that clearly states the solution

CCSS – OA Represent and solve problems involving addition and subtraction. 1.Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

CCSS – OA Represent and solve problems involving addition and subtraction. 2.Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Modeling Daily Math Renee and Pam Word Problems

Add To – Result Unknown There are seven children playing at the park. Four more children come to the park. How many children are in the park now?

Taken From – Result Unknown There are thirteen children playing at the park. Seven children goes home. How many children are in the park now?

Put Together/Take Apart – Total Unknown At the park, 8 children are in the playground and 5 are by the pond. How many children are in the park?

Put Together/Take Apart – Both Addends Unknown There are 16 children in the park. They are at either at the playground or by the pond. How many are at the playground and how many are by the pond?

Put Together/Take Apart – Both Addends Unknown Rene has 14 bears. They are all red or blue. How many red bears and how many blue bears could she have?

Add To – Change Unknown Renee has nine games. She got some more games for her birthday. Now she has 15 games. How many games did Renee get for her birthday?

Taken From – Change Unknown Renee has 12 stuffed animals. Her new puppy got loose and chewed up some of them. Now she has only 9 stuffed animals. How many stuffed animals did the puppy chew up?

Multiplication There are 3 boxes. Each box has 4 cookies in it. How many cookies are there in all?

Group Size Unknown Renee has 15 cupcakes. She arranges them on three plates so that there is the same amount of cupcakes on each plate. How many cupcakes are on each plate?

Number of Groups Unknown Renee bought 12 extra pencils to give to her best friends. If she gives each of her best friends 4 pencils, how many best friends does she have?

Renee – Modeling Daily Math Shapes Time Money

Daily Math, continued Geometry Plane Shapes: Rectangles, Squares, Triangles, Trapezoids, Half-Circles, Quarter- Circles Solids: Cubes, Right Rectangular Prisms, Right Circular Cones, Right Circular Cylinders Be able to identify critical attributes Continue to review shapes from K

CCSS – Geometry Reason with shapes and their attributes. 1.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.

Daily Math, continued Graphs and Data At least once a month – related to things about the kids Graphs represent real people and real data Ask a wide variety of problems related to the graph including “What would happen if….” questions

CCSS – MD Represent and interpret data. 4.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.

Daily Math, continued Time Morning, afternoon, evening, am, pm Order of events To the nearest 5 minutes (depends on grade level)

CCSS – MD Tell and write time. 3.Tell and write time in hours and half-hours using analog and digital clocks.

Daily Math, continued Money Names of Coin Values of Coin

Addition and Subtraction Facts

CCSS – OA Understand and apply properties of operations and the relationship between addition and subtraction. 3.Apply properties of operations as strategies to add and subtract. 3 Examples: If = 11 is known, then = 11 is also known. (Commutative property of addition.) To add , the second two numbers can be added to make a ten, so = = 12. (Associative property of addition.) 3

CCSS – OA Understand and apply properties of operations and the relationship between addition and subtraction. 4.Understand subtraction as an unknown- addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.

CCSS – OA Add and subtract within Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

6.Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., = = = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding by creating the known equivalent = = 13).

CCSS – OA Work with addition and subtraction equations. 7.Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, = 2 + 5, =

CCSS – OA 8.Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 =  – 3, =.

Teaching for Understanding Telling students a procedure for solving computation problems and having them practice repeatedly rarely results in fluency Because we rarely talk about how and why the procedure works.

Teaching for Understanding Students do need to learn procedures for solving computation problems But emphasis (at earliest possible age) should be on why they are performing certain procedure

Research Students who learn rules before they learn concepts tend to score significantly lower than do students who learn concepts first Initial rote learning of a concept can create interference to later meaningful learning

Gretchen – 1 st Grade 70 – 23

Progression Concrete Pictorial or Visual or Representational Abstract  Invented Algorithms  Alternate Algorithms  Traditional Algorithms

Invented Procedures Allow students to invent and develop their own procedures based on what they already know

Fact Fluency Fact fluency must be based on understanding operations and thinking strategies. Students must  Connect facts to those they know  Use mathematics properties to make associations  Construct visual representations to develop conceptual understanding.

Math Facts Direct modeling / Counting all Counting on / Counting back / Skip Counting Invented algorithms  Composing / Decomposing  Mental strategies Automaticity

Addition

3 + 2 

4 + 3  

 

Domino Facts

Tens Facts   = 10

7 + 5    

8 + 6      

Addition – Make ten

Addition – Make ten

Addition –

Make tens

Addition –

8 ones + 6 ones = 14 ones 14 ones = 1 ten + 4 ones tens + 1 ten = 3 tens 3

Adding 2-digit numbers Miguel – 1 st Grade Connor – 1 st Grade How is the way these students solved the problems different from the way we typically teach addition?

Addition Try at least 2 different strategies on each problem

Vertical vs Horizontal Why do students need to be given addition (and subtraction) problems both of these ways? =79 + 5

Subtraction

1. Katie had 5 candy hearts. She gave 2 of them to Nick. How many hearts does Kate have left for herself? 2. Katie has 5 candy hearts. Nick has 2 candy hearts. How many more does Katie have?

5 – 2 

 

– 2

– 2

Subtraction How do you currently teach subtraction?  “Take-away”  “The distance from one number to the other” Additional Strategies

Subtraction: 13 – 6 Decompose with tens 13 – 6 = 13 – 3 = – 3 = 7 33

Subtraction: 15 – 7 Decompose with tens 15 – 7 = 15 – 5 = – 2 = 8 52

Developing Subtraction Connor – 1 st Grade 25 – 8 Connor – 1 st Grade 70 – 23

Subtraction: 43 – 20 Take Away Tens 43 – 20 = 40 – 20 = 20so 43 – 20 =

Subtraction: 43 – 20 Count back 43 – 20 = 43, 33, 23

Subtraction: 43 – 20 Count up 43 – 20 = 20, 30, 402 tens 41, 42, 433 ones 23

Subtraction: 53 – 30

Subtraction: 53 – = =

Subtraction: 53 – 30

Subtraction: 73 – 6 Regrouping and Ten Facts 73 –

Subtraction: 42 – 9 Regrouping and Ten Facts 42 –

Exploring Resources Doc Locker Illustrative Mathematics