Assessing what “Counts”

Hunter at the end of Kindergarten He can count to 100 and he knows all of his shapes. His teacher says, “He’s doing great in math”. What Hunter’s teacher doesn’t know … Hunter can’t accurately count out a pile of 32 objects.

Hunter at the End of 1st Grade Hunter can add and subtract and Can solve word problems His teacher says, “His math skills are strong” What Hunter’s teacher doesn’t know … Hunter doesn’t see groups, he still thinks of everything as one.

Hunter at the End of 2nd Grade Look at Hunter now! By the end of 2nd grade, Hunter can add and subtract two-digit numbers. His teacher says he needs more work with addition and subtraction because he’s not always accurate. What Hunter’s teacher doesn’t know … Hunter doesn’t understand how to compose and decompose numbers.

Hunter at the End of 3rd Grade By the end of 3rd grade, Hunter is really struggling in math. He’s having a very hard time understanding the concept of multiplication, and often tries to hid the fact that he’s counting on his fingers to add and subtract. What happened to Hunter?

Do our Current Assessments… …tell us if our K-2 student have missed critical understandings?

Assessing Math Concepts It is not enough to know if the child can get right answers. We need to know what mathematics the child knows and understands. Have one leader read this slide. ©Math Perspectives Teacher Development Center, Bellingham, WA www.mathperspectives.com 7

AMC Assessments Inform instruction Document growth Uncover the child’s edge of understanding Help us understand how children construct mathematical understandings Ask a participant to read the first bullet, then another participant to read the second, and so on.

From Counting, to Seeing/Using Groups, to Knowing Combinations How many of you get students each year who seem like they aren’t ready for 2nd grade math? One of the first assessments you will do in 2nd grade is the hiding assessment. This assessment will help you determine what they need.

Moving Away from Counting All As you watch the video, consider… … does the student see groups? … how does he determine the total? http://www.youtube.com/watch?v=UdLNTikXmIc&app=desktop Start at 1:26, End at 2:33 http://www.youtube.com/watch?v=UdLNTikXmIc&app=desktop Start at 1:45.

Number Arrangements Assessment The goal of number arrangements is to recognize the parts of numbers and to combine the parts of numbers without counting all. How could this assessment help you to better understand, our previous student, Isaiah’s learning needs? Explain number arrangements, hold up number arrangement cards for the class to see http://www.youtube.com/watch?v=UdLNTikXmIc&feature=youtu.be Ask participants to turn and discuss video.

Let’s Try an Assessment Log on to www.amcanywhere.com District ID: 9001 User Name: Your 5-digit CMS ID Password: Watch and discuss the video for 32 first. Then watch the video and remodel for 21. Ask, what did you notice when he said “12” as he was counting? Why is that important? Would that be an example of conservation of number? Show video for 12 and ask teachers to assess on own. Ask, “how is his counting different when presented with 12?” Make sure participants notice Corey is more confident, he doesn’t line them up because he doesn’t need to, 12 is comfortable for him.

Click “Start Assessment” at the top of the page

What Can the Reports Tell Us? What instructional moves does the author suggest for a student like Corey? Look at the table at the top of the page.

Explain how to read an AMC report

Combination Trains Assessment Learning Number Combinations Children need to see the basic facts as a set of interrelated concepts. Children need to be able to look for relationships between the facts they know and other larger, more complex numbers or problems. Emphasis needs to be on learning number composition and decomposition and number relationships – not just on getting the right answers. Common Core Alignment: 1.OA.3; 1.OA.5; 1.OA.6 What are we trying to determine with this assessment? To determine what number combinations the student knows and to find out if they can use the answer to a combination they know to figure out one they don't know. Does student know the parts of numbers to 10? Can student use efficient strategies to solve problems to 20.

How Children Learn Number Concepts Watch Harper Read the selection: Combining Parts of Numbers When finished, silently reflect about Harper. Where does Harper fall within these critical learning phases? Watch Isaiah’s video. Read Article: Combining Parts of Numbers from How children learn number concepts Ask participants to turn and talk about Harper. Script from video:   Harper: Blue- 4, 2 and 2, 2 plus 2 = 4 Yellow- 5, 5 is one more than 4 Altogether- 9, 5+4=9 Blue- 6, 3 and 3 Yellow- 7, 7 is one more than 6 Altogether-13, 5+5=10 and 2+1=3; I used the 2 leftover from the 7 and 1 leftover from the 6 Blue- 8, 4 and 4 Yellow- 8 Altogether- 16, 5 and 5 then 3 and 3 What is there 9 yellow- 17, 9 is only one more than 8

Assessment Practice Find a Partner Arrange the three combination trains Teachers will take turns giving the assessment while their partner plays the role of the child, then they switch.

How Children Learn Number Concepts Watch Isaiah Discuss: Which phase would best help him succeed? Isaiah: Blue- 4, I knew in my mind it was 4 Yellow- 5 (he counts them silently) Altogether- 9 (counts them all silently after saying answer) Blue- 6 (counts with eyes but says he just knows) Yellow-8, asked again to count, does with finger and taps with finger then counts aloud without finger then prompted Altogether- 13, I know in my head but then he counted back from 7 Blue- 8 counts individually Yellow- 8 counts again Altogether-  

From Combo trains to number parts

Hiding Assessment How is this different from flashcards or timed tests? (Hint: see pages 102-103 in your blue book)

Watch Emily -What changes do you notice? When presented When presented with 5 http://www.youtube.com/watch?v=7VgYCumqAIc -What changes do you notice? When presented with 6 http://www.youtube.com/watch?v=7VgYCumqAIc -What are her counting behaviors? Watch and discuss the video for 32 first. Then watch the video and remodel for 21. Ask, what did you notice when he said “12” as he was counting? Why is that important? Would that be an example of conservation of number? Show video for 12 and ask teachers to assess on own. Ask, “how is his counting different when presented with 12?” Make sure participants notice Corey is more confident, he doesn’t line them up because he doesn’t need to, 12 is comfortable for him.

AMC Blue Book-combo trains Please preview pages 101 – 111. What do you notice about the information in the book? How can this book help you better understand a student’s needs? AMC Blue Book-combo trains Introduce Book: Each section is laid out in a similar fashion. First the section discusses the goals of the assessment, students number development, explains steps of the assessment, and finally linking the results to the instruction.

Hiding Assessment Learning to Decompose Numbers To subtract children need to know the parts of numbers and see the relationship between composition and decomposition. Children must recognize that one number is contained within another number. Children must understand that the number stays the same even when it is broken apart and recombined in various ways. Common Core Alignment: 1.OA.3, 1.OA.4, 1.OA.5, 1.OA.6 What are we trying to determine with this assessment? If a student know parts of numbers to 10 quickly without having to count them to figure it out Can students use what they know about parts of numbers to solve a subtraction problem

Hiding Assessment Libby Part 1 – Hiding with Counters Part 2 – Hiding without Counters Note: Go to Part 2 after you have finished Part 1. Assess only the numbers the student knew (Ready to Apply); this is confirm student can identify parts of numbers mentally and are flexible in their thinking about numbers. Part 3 – Log into demo mode and practice the Hiding Assessment with a partner. Watch video of Libby with Hiding Assessment then allow teachers to practice with each other.

From Hiding to Known Combination to get to a ten!

Ten Frames Assessment Learning about Numbers as One Ten and Some More Understanding that numbers are made up of “ten and some ones” is a foundational skill students must learn to work with larger numbers. To solve more challenging problems student must move beyond counting on strategies and be able to solve problems by using relationships and understanding the underlying structure of numbers to 20. Common Core Alignment: 1.OA.3 & 1.NBT.2 What are we trying to determine with this assessment? if the student can combine single digit numbers by reorganizing them into a 10 and leftovers. if the student can use their knowledge of the parts of numbers to 10 to subtract numbers up to 20.

Tens Frame Assessment Click on the picture to go to the link http://www.youtube.com/watch?v=FGfj9oPaJW0 Discuss what you observe in the video

What are we trying to determine with this assessment? Ten Frames Assessment What are we trying to determine with this assessment? Can the student combine a ten and some ones without counting and can the student combine numbers by making a ten and leftover ones? Can the student decompose a teen number into a ten and leftovers and can the student subtract by breaking up a number in order to get to ten, and then subtract what is left from 10? Now it’s your turn to practice the assessment with a partner!

From Tens frames to Grouping tens

Grouping Tens Assessment Learning about Numbers as Tens and Ones Children need to learn that numbers to 100 are composed of groups of tens and ones. Children must do more than label the digits in a number – they must understand that numbers are organized into groups of tens and ones. Children must recognize that a ten is both one ten and ten ones. This level of thinking is difficult for young children. CC Alignment: 1. NBT.2; 1. NBT.4; 1. NBT.5; 1. NBT.6 What are we trying to find out from these assessments: Do students understand that numbers to 100 are organized in groups of tens Can they add tens without counting Can they take away tens without counting Do they understand that counting by groups does not change the total quantity

Grouping Tens Assessment: Let’s look at Reggie Click on picture for video link. Watch video, pause periodically and discuss http://youtu.be/5A-f4Og4Uuk

What are we trying to determine with this assessment? Grouping Tens Assessment What are we trying to determine with this assessment? Can the student decompose numbers to 20 into tens and ones, by showing the value of the 1 in the tens place in teen numbers and by telling the number leftover when ten is removed from the teen number? Can the student tell how many in a quantity if the number of tens and ones is known and if the student can add and take away ten without counting? Can the student add and take away groups of ten to 2-digit numbers? Log into demo mode and practice Grouping Tens with a partner. Participants will practice grouping tens with a partner.

How do I find appropriate activities according to my data? Read pages 188 – 194 in your blue book called “Guidelines for Providing Appropriate Experiences”. After reading, have teachers count off by 3 to 5 (depending on the size of your group) using “Tribal Numbers” to form their groups. **See if they can count off without giving them the tribal numbers as a resource first.** Once they are in groups, have them compare and contrast the two teaches from the blue book.

Class Instruction Report – lets you know which students have similar needs Talk about how to group students/recognize their needs This data follows the child from grade to grade – you will have previous year’s data in the system

Class Summary Report – can give you information about where you would start with the beginning of the year assessments or if you need to progress monitor in the middle of the year/for anyone who may push-in and test your students – gives them a starting point

Useful for report cards

How do I set up my room for AMC? Setting up workshop in Investigations Practice, practice, practice routines Using working levels to ensure students are working independently and quietly Meet with one small group a day, use the rest of the time to assess or progress monitor 3-4 students in the class. Pass out the Working Levels Handout – Have participants read and discuss Working levels – you could use these levels for students to self-evaluate themselves after workshop…were you a 0, 1, 2, 3, or 4? (this comes from Kathy Richardson’s book) One teacher had students self-evaluate themselves and then put the teacher’s number underneath. Everyone was a 3 unless I came around and let you know otherwise (during workshop you may have to talk to some students who are off task, too loud, etc.)

Working Level Board Example Working level board – an example of a way you can show students working range of numbers