Building a Solid Number Foundation Strategies for Education Assistants Session 3 Assessments and Strategies

Informal Assessments Research based: From First Steps in Mathematics (Pearson Educational) Big Ideas from Dr. Small (Nelson Publishing)

Number “Big Ideas” Numbers tell how many or how much Classifying numbers provides information about the characteristics of number There are different but equivalent representations for number (Part-Part-Whole) We use a number system based on patterns Benchmark numbers are useful for relating and estimating numbers

Counting Beginning at 1, start counting for me…. Listen carefully….

Let’s Watch… Early Childhood Counting Kindergarten Counting Assessment

Get Me Task Purpose Procedure Observe To see if students choose to use counting when asked to get a number of items Procedure Tell the child that you need some blocks to play a game. Ask, Can you get me 7 blocks? Observe Do they choose to use counting to help find the right amount? Do they grab a handful and ignore the amount requested?

Some students find the ‘get me’ task quite difficult… because… they have to remember the number word, then count out the number of items, and monitor for the requested number while they count. (Baroody and Wilkins 1999)

If children do not know the number string well… their working memory is taken up with remembering the sequence, and they tend to forget the number that they were asked to get.

Counting on… Counting on reduces cognitive load. Counting on is linked to the idea of quantity Linked to counting on is part whole understanding

Written numbers Have students fill in the missing numbers: 1 3 9 1

Student responses using the informal assessment show what all students understand.

Write and Say Say these numbers. Have the student write them: (answer) [misconception] Sixty-four (64) [604] One thousand twenty (1020) [100020] Two thousand six hundred fifteen (2615) [200060015, 2000650] Five hundred six thousand fifteen (506 015) [500600015] One million five (1000005) [10000005]

Look for…. Number (digit) reversals Misplaced numbers in the teens and after 20 Incorrect number form after 99 (1001, 1002 etc) Start at 100 instead of 1 to see how the student writes the numbers beyond 100 and into the other 100s

Understanding the Pattern of Numbers Students need to: Memorise 1, 2, 3, ….9, 10, 11, 12, 13. Hear the 4-9 in 14, 15, 16, 17, 18, 19 Predict and name the decades Repeat 1-9 in each decade Predict and name the hundreds Repeat the decade and 1-9 sequences in each of the hundreds 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 Number Sense

What to do? Play games that involve chanting the numbers Use number lines (Organic Number Line) Create number scrolls (use the constant function on a calculator to help) Play biggest number or next number Use a 100 chart to look for patterns Bicycle Odometer

Sometimes students learn ideas we do not intend to teach them. Reflect on where you begin counting when the collection is in a line. Do we always count that way? What training do we focus on in teaching children to read and write?

Strategies: Add to your Concept Map or Mind Map as we move through the different strategies. Which strategies might help specific students who you work with develop stronger mathematical understanding?

Numbers tell how many/how much

Recognizing at a glance…

Place Value Students can often get through a worksheet correctly…. but…….

582 - 198 Use partitioning to mentally solve this problem. Record how you solved it. Be prepared to share your strategy.

582 - 198 582 = 500 + 80 + 2 582 = 200 + 382 Standard partitioning Non-standard partitioning  582 = 200 + 382 Helps us to subtract 198

Wipe out Enter a number such as 256 into the calculator. How can we make the 5 a zero? Why did you do that? What number have we got now? How can we make the 2 a zero? What number have we got now? How can we make the 6 a zero? Students can play wipe out in pairs taking turns to give each other the instructions. First Steps in Mathematics

Can I Have All Your…….? Play with a partner Choose a 3-digit number Partner A asks: “Can I have all your 8’s? Partner B says either: “You can have nothing” or “You can have 80.” Partner B subtracts 80. Partner A adds 80. Winner reaches exactly 1000 or opponent reaches 0.

Number Concept

Which number does not belong? Why? 4, 16, 36, 48, 64, or 81

4 “It’s only one number. The rest are two.” “it’s the only number less than 10; the rest are between ten and one hundred.” “it’s only one digit; the rest are two-digit numbers.” “it’s the four.” 81 “Eighty-one is an odd number. All the others are even numbers.” “Eighty-one is not divisible by four. All the other numbers are multiples of four.” “You can’t get to 81 with just these numbers.” 64 ÷ 16 = 4, 64 ÷ 4 = 16, 48 – 16 + 4 = 36, 64 – 16 = 48, 16 x 4 = 64 ….. 48 “it’s the only one that is not a square number.”

How does the task “Which Does Not Belong How does the task “Which Does Not Belong?” help you to learn more about what your students know and how they solve problems? How did your thinking grow and change as you listened to your peers? How does knowing the “big ideas” help with understanding student thinking?

Task: On your “Sticky note”: Write a number between 1 and 1 000 000 000 Represent your number in another way Organic number line (example) Number concept and place value

“Organic number” line…a number has many forms…

Scaffolding = Differentiation Temporary supports that allow students to accomplish tasks that they otherwise would be unable to complete

Some ways learning can be scaffolded include: Teaching Strategies Questioning Strategies Student Collaboration Whole-group Discussions Making Connections Explicit Graphic Organizers

How are a square and cube..... Same Different Word Bank Angle Face Three-dimensional Cube Degrees Rectangular Prism Edge Side Two-dimensional Square Vertices vertex

There are some bicycles and tricycles. There are 14 vehicles There are some bicycles and tricycles. There are 14 vehicles. There are 34 wheels. How many bicycles are there? How many tricycles are there? Facts: Drawings: Computation: Answer:

Vocabulary…. Understanding mathematics vocabulary is directly related to mathematics success. We must teach common vocabulary to our students Necessary vocabulary is included in every unit the the current mathematics text books

Strategies Frayer Model Word Banks/Word Walls Internet Field Trip Literature (story books)

Your Role: Listen to what students say Watch what they do Ask questions Respond carefully Provide talk time Allow students to struggle

Reflection…. Think about several students who you work with. Which informal assessments could you use with them and which strategies could you try to further their mathematical understanding? Discuss your ideas with the people at your table.

For Next Time…. Try several informal assessments and strategies with your students. Were they successful, what did you learn, what do you need to more about?

Option #2 What was the most interesting task introduced in this session? How will you use it with students?

Please Note: If you are doing the summative assessment in order to receive a certificate, please bring your assessment and a self-addressed stamped envelope to session 4(unless other arrangements are made to return assignments and issue certificates).