K-2 Math Night Developing strong math thinkers….problem solvers of the future! We want students to know how to compute…but more importantly, we want them to know how to think and understand how numbers fit together. We live in an age where Siri can answer any question like this in seconds. Of course, students need to know how to do this math, but we want them to be able to think about how numbers work. Look at this problem… How does this problem relate to the work K-2might be doing? Presented by: Beth Finkelstein, K-5 Math Staff Developer Alaura Imperioli, Kindergarten Teacher Alissa Schaps, Kindergarten Teacher

Pelham Public Schools K-2 Math Presentation Agenda Pedagogy of Eureka Math K-2 & Math in Focus 3-5 Developing Flexible Math Thinkers Kindergarten First Grade Second Grade Supporting Your Child in Math at Home Presented by: B. Finkelstein,A. Imperioli, A.Schaps, J.Denet, C. Cavalli

Pedagogy of Math in Focus and Math Modules For students to develop a deeper understanding of the mathematics, we do not just want to show them the steps or algorithm to memorize. We want them to first have a concrete experience with manipulatives so they can see what is happening (Concrete). Then they take that experience and interpret their understanding and communicate their understanding through a visual representation (Pictorial). This might be drawing a picture or symbols. At the early level this might be drawing circles to represent a quantity. As students progress and the numbers get larger they begin to use symbols (e.g. a line to represent a group of 10, or circles with 1, 10, 100,… to represent the place value chips. ) As students progress through these stages, the teacher continues to show them the abstract symbols (the equation or algorithm). This way, students can begin to see the connections and have a deeper understanding of what is happening when they use the algorithm. (Good example: Adding with regrouping…Use base 10 blocks for students to see what happens when you have more than 9 ones…you can regroup and take a 10 rod. This is what happens when we put the little one above the 10s column). file:///H:/My%20Documents/013-014%20Math%20Staff%20Development/2014-2015%20September%20Info/Building%20Mathematical%20Understanding.pdf

What is fact fluency? So how does fluency fit into all of this? It is useful to hold some math facts in memory…many in fact! To know or figure math facts quickly so we don’t get caught up in the other math thinking we need to do. But to get there, we want students to learn math facts through using them in different mathematical situations, not just by practicing them out of context such as memorizing tables. We want our students to have number sense, something that is much more important for students to learn, and that includes learning of math facts along with deep understanding of numbers and the ways they relate to each other. We want them to see the related facts and how they fit together, not as individual facts in isolation. We want them to see the relationship between addition and subtraction/ multiplication and division so our work focuses on the numbers and what happens to the numbers and how we can manipulate numbers.

Kindergarten Counting with 1:1 correspondence Comparing two sets of objects

Kindergarten Master Facts within 5 Work on Facts to 10 4 1 5 Students have been working with the concrete. We are beginning to move them into pictorial- representing rabbits in the drawing of the cube stick. 4 1 5

Kindergarten: Number Bonds 5 1 4

You’ve gotten very good at showing fingers the Math way You’ve gotten very good at showing fingers the Math way. I want to challenge you to think of other ways to show numbers on your fingers. First, I’ll ask you to show me fingers the Math way. Then, I’ll ask you to show me the number another way. Show me 2! Now show me another way to make 2 using two hands. How can we be sure that we're still showing 2? Count the fingers on both hands.

Kindergarten: Composing and Decomposing Numbers What do you notice about the two equations in each problem? Why do you think this is done?

Kindergarten 5-Group Way Numbers 6-10: Use 5 as a Benchmark Number Students learn to look at the 5 groups and think “Where can I take the 3 from?...Where can I take the 5 from?” This is training their thinking for later work with subtracting from teens when they have to think “Can I take from the ones or do I need to take from the 10?”

Kindergarten 5-Group Way Numbers 6-10: Use 5 as a Benchmark Number Students learn to look at the 5 groups and think “Where can I take the 3 from?...Where can I take the 5 from?” This is training their thinking for later work with subtracting from teens when they have to think “Can I take from the ones or do I need to take from the 10?”

Kindergarten: Use 5-Group Cards to Make 10

First Grade: Master Facts within 10 Work on Facts within 20 Review and use knowledge from kindergarten of number combinations within 10. Focus on combinations of 10: Knowing all number bonds for 10. Associative property: Group in different ways 5+1+9= 5 + (1+9) Commutative Property: Move addends (or factors) around: 3+5 = 8 5 + 3 =8 5 +1 +9 = 9 +1 +5

First Grade: Make a 10 Strategy Jack has 8 raisins. Jenny has 4. How many raisins do they have in all? Video: Make a Ten (begins…”I took eight and put it on the Ten Frame…”

1st Grade: Make a 10 Strategy (Decompose a Number)

First Grade: Subtraction: Taking from a Ten 8 Of course we want them to begin to learn that 16-8 =8, but this is also an opportunity to develop an understanding that will help with regrouping in second and third grade. Think about the problem 56-8. We want students begin to question…do I have enough ones, in this case to take 8 ones from 6 ones? 10 6

First Grade: Place Value, Tens and Ones

Fluency with 2-digit addition and subtraction within 100 Second Grade Fluency with 2-digit addition and subtraction within 100 Understanding the value of each digit Learn a variety of strategies: Build understanding Evaluate: What is the best strategy for me? At this time of the year, second graders should know their addition and subtraction facts within 10 and by the end of the year know their facts fluently within 20. What does fluently mean? In the case of 6+4 it should be automatic…but we want students to develop fluency for working with larger numbers too! Efficient strategies- automatic and/or strategy for solving quickly.

Place Value Chart with Base Ten Blocks Place Value Chart with Place Value Disks

Second Grade: Place Value Students spend a lot of time building numbers with manuipulatives and identifying the hundreds, tens and ones. Here a student would draw 96 using place value and box it to show what they started with. Then they would count on to the next benchmark number (10’s or 100’s) Understanding the value of each digit

Second Grade: Place Value Just as students were decomposing a teen number into a ten and ones, now they are looking at 3-digit numbers and decomposing the numbers into place value. Numeral: 145 Word form (number names): One hundred forty five Unit form: One hundred four tens five ones Expanded form: 100 + 40 + 5 Unit value of 4 in 145: 40 3 hundreds 3 tens 3 ones Expanded form: 300 + 30 + 3

Second Grade: Place Value Open Number Lines Use each number line to show a different way to count from $580 to $994. Students will also spend time adding 10’s and 100’s to a number, applying what they know from earlier knowledge…for example if 4 and 5 is 9, then 4 tens and 5 tens is 9 tens. The open number line lets children apply this number knowledge in counting between numbers. Again, the benchmark numbers, 10’s & 100’s are helpful here!

Second Grade: Place Value Open Number Lines Use each number line to show a different way to count from $580 to $994. Again, the benchmark numbers, 10’s & 100’s are helpful here!

26 + 30 = 56 Second Grade: Add and Subtract 10 and 100 Open Number Line 26 + 30 = 56

26 + 30 = 56 Second Grade: Add and Subtract 10 and 100 Arrow Way 26 + 30 = 56 This works the same way for subtraction too! We use the arrow way, because it is not a balanced equation to write: 26+10=36+10=46+10=56

56 - 30 = 26 Second Grade: Add and Subtract 10 and 100 Counting On 56 - 30 = 26 Count up from 30 to 56. Students learn the relationship between addition and subtraction.

Second Grade: Add and Subtract 10 and 100 Number Bonds All that work of understanding place value and composing and decomposing numbers to make a ten comes together to help them work with larger numbers. So how can knowing the bonds for 26 help? 20 + 30 = 50 50 + 6 = 56

Second Grade: Add and Subtract 10 and 100 Number Bonds 56 - 30 = 26 We can use this too to help with subtraction. 50 - 30 = 20 20 + 6 = 26

Second Grade: Number Bonds- Decompose Numbers = 67 47 + 20 = 67 As they learn to add 10, 20, …100 to a number, they can look for ways to make these friendly numbers and begin to easily manipulate numbers to add and subtract. 48 + 21 = 69 40 + 20 = 60 8 + 1 = 9 60 + 9 = 69

Leading to…mentally adding and subtracting 10’s or 100’s 27 + 29=

How do you do this mentally? Think about… 29 + 46 = …did you think… 30 + 45 = 75 ? Or perhaps you thought 20 + 40 = 60 9 + 6 = 15 60 + 15 = 75 How do you do this mentally?

How do you do this mentally? Think about… 28 + 36 = …did you think… 30 + 34 = 64 ? Or perhaps you thought 30 + 20 = 50 8 + 6 = 14 50 + 14 = 64 How do you do this mentally?

Second Grade 38 + 24 = Adding with Regrouping Using Place Value Disks: Building our understanding for the algorithm Video Link: Adding with Place Value Disks 38 + 24 = Tens Ones 2 6

Second Grade 45-17 Subtracting with Regrouping Using Place Value Disks Video Link: Subtracting with Place Value Disks

Second Grade: Leading up to understanding the algorithm Totals Below New Groups Below 1 2 4 + 3 8 1 2 4 + 3 8 1 2 5 0 + 1 0 0 New Groups Below…think about 4+8= 12…how do you write the number 12? 1 then 2… We use the language: 20 +30 or 2 tens and 3 tens 1 6 2

Questions to Ask Students What do you know? What can you start with? Can you tell me the story? (good for word problems) What would that look like? How is this similar to the one you did before? How is this different from the one you did before? Are you sure? How do you know? Can you think of another way to show it? If you have a strategy…it is okay to share that too: Try, “Here is how I am thinking about it… How do you see it? Rather than accepting “I don’t know” or “this is too hard” we can move students along and give them an entry point by asking them some questions.

Kindergarten and First Grade Activities to Try at Home Roll one or two dice and collect that many objects. Roll one die and tell how many more to make 10. Roll one die and count on for 3 numbers. Pick two cards out of a deck and say which number is more. Say what comes next in a sequence (17, 18, ___), (___,8, 9) or 6, ___, 8. Show different ways to make combinations of a number using your fingers or objects. Use everyday objects to count. Make groups with a collection of objects. Play math games with your child. For example, “I’m thinking of a number. It comes after 5. What is the number?” or “I’m thinking of a number. It comes before 9. What is the number?”

First and Second Grade Activities to Try at Home Look for everyday opportunities to have your child do mathematics. For example, if you open a carton of eggs and take out seven, ask, “How many are left in the carton?” Play math games with your child. For example, “I’m thinking of a number. When I add five to it, I get 11. What is the number?” Encourage your child to read and write numbers in different ways. For example, what are some ways that you can make the number 15? 15 can be 10+5, 7+8, 20-5, or 5+5+5. Have your child create story problems to represent addition, subtraction, and comparisons. For example, “I have seven pennies. My brother has five pennies. How many pennies does he need to have the same number as I have? He needs two more pennies.” Ask your child how many more they need to get to the next 10 or 100… Say, “I have 137. How many more to get to 150?” or “I have 23. How many more to get to 30?...How many more to get to 100?”