1 K-8 Mathematics Standards Content Training Counting and Number Relationships

 Valerie Adams, Math Coach, Intervention Specialist, Virgie Robinson Elementary School, Pasco School District  2

 Develop understanding of counting and number relationship standards for your grade band.  Develop understanding of development of counting number concepts.  Learn a variety of strategies for developing counting and number relationships with students.  Experience counting and number activities related to standards. 3

 Allow ourselves and others to be seen as learners.  Monitor own airtime and sidebar conversations.  Allow for opportunities for equitable sharing.  Presume positive intentions.  Be respectful when giving and receiving opinions, ideas and approaches. 4

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For all students to learn significant mathematics, content should be taught and assessed in meaningful situations. 6

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 Conceptual Understanding ◦ Making sense of mathematics  Procedural Proficiency ◦ Skills, facts, and procedures  Mathematical Processes ◦ Using mathematics to reason and think 8

 At each grade level: ◦ 3-4 Core Content areas ◦ Additional Key Content ◦ Core Processes (reasoning, problem solving, communication)  For each of these: ◦ Overview paragraph ◦ Performance Expectation ◦ Comments/Examples 9

 Use either your Standards Document or Strands Document to find all K-8 references to counting and number relationships  Go back and carefully read the Performance Expectations and Explanatory Comments and Examples for your grade level.  Note the expectations for the grade level above and below yours. 10 What should your students already know? What do you need to teach this year? What do they need to know for next year? What should your students already know? What do you need to teach this year? What do they need to know for next year?

 Often called instant recognition  Knowing how many in a collection without counting  Develops before counting and supports counting  Children often do not benefit from counting experiences before they can subitize small numbers  Can be undermined by counting 11

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What does it mean to say someone can count?  To say the names of the numbers in order.  To count a collection of objects one by one and tell how many.  Each of the two meanings has their own set of concepts and skills.  The two concepts must come together for students to understand quantity. 13

14  Each object must be counted only once as the numbers are said.  The numbers must be said once and always in the conventional order.  The objects can be touched in any order and the starting point and order in which the objects are counted doesn’t affect how many there are.  The arrangement of the objects doesn’t affect how many there are.  The last number said tells ‘how many’ in the whole collection, it does not describe the last object touched. (FSiM) K.1.E

“Get me 8 blocks” Requires students to:  Remember the number word.  Count the number of objects.  Monitor for the requested number while they count. If a child’s working memory is taken up with the counting sequence this task is quite difficult. 15 K.1.E

While visiting another civilization we learned their way of counting. We can use the digits 0, 1, 2, 3, 4 only. When we have one more than 4, that number is called Zirkle and it moves to a new “place”. The counting sequence looks like: 1, 2, 3, 4, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24, K.1.A-G 1.1.A-C 1.1.E 2.1.A-G K.1.A-G 1.1.A-C 1.1.E 2.1.A-G

We say the numbers like this: One Two Three Four Zirkle Zirkle one Zirkle two Zirkle three Zirkle four Two zirkle 17

 Write the numbers from 1 to 200 and circle any patterns you see.  Create a number line from  Count the objects in the bag and write how many.  Show 33 cubes.  Find three more and three less than 23 on the number line.  Start at 43 and count backwards.  Discuss in your group:  What did you need to keep in mind while doing the tasks? Which tasks were the most difficult for you?  What patterns did you see? 18 K.1.A-G 1.1.A-C 1.1.E 2.1.A-G K.1.A-G 1.1.A-C 1.1.E 2.1.A-G

19 30 minutes

Students need to:  memorize 1, 2, 3, ….9, 10, 11, 12, 13.  hear the 4-9 in 14, 15, 16, 17, 18, 19.  predict and name the decades 10, 20, 30…  repeat 1-9 in each decade 21,22,23,24…  predict and name the hundreds 100, 200, 300.  repeat the decade and 1-9 sequences in each of the hundreds 234, 235, 236…  predict and name the thousands.  repeat the hundreds, decades and 1-9 sequences within each of the thousands.  say the places in order from left to right. 20 K.1.A K.1.D 1.1.A 1.1.E 2.1.A 2.1.E K.1.A K.1.D 1.1.A 1.1.E 2.1.A 2.1.E

 Saying the counting sequence to a rhythm or actions helps us remember the sequence.  The rhythm should be close to the speed of heart beats.  Using the same rhythm and actions to skip count helps children explore the relationships between numbers, 2, 12, 22, 32…  Exploring the patterns in numbers helps us see relationships among numbers and helps us understand the number system. 21

A 2.1.A 1.1.A 2.1.A

2 4 Daniel’s counting by 2’s The quantity remains the same no matter how you count it. 23

24 K.1.A 1.1.A 2.1.A K.1.A 1.1.A 2.1.A Counting by a given number from any start point START with 3 and JUMP 5. Go up to about 130 Record each landing number. 3, 8, 13… Change the START and see what happens. Keep the START at 3 and change the jump. What happens? What patterns do you see?

 Both use 0-9 pattern and ones, tens, hundreds, thousands… Some differences:  -teen, -ty for ten  11, 12,… no tens or ones marked  thirteen and fifteen, different pronunciation than three and five, ones first then “teen”  We explicitly say the value of the numbers in hundreds, thousands… one thousand, four hundred twenty-three.  1423 The value of the numeral is implied by the position K.1.B 1.1.C 1.1.E 2.1.E K.1.B 1.1.C 1.1.E 2.1.E

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 Thinking about the Big Ideas, Strategies and Models from tonight, record in your Journal:  Something new I learned  Something I want to try  Something I am still wondering about 28

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 First Steps in Mathematics: Number  Elementary and Middle School Mathematics, John A. Van de Walle  Developing Mathematical Ideas(DMI), Building a System of Tens, Schifter, Bastable, Russell  Math Their Way, Mary Baratta-Lorton 31