Welcome to Building K-1 Number Sense

Lynne Allen – Wake County

North Forest Pines Elem – 1st Grade

Common Core Standards

• K – Counting and Cardinality (K.CC.1-K.CC.7)

• K – Number and Operations (K.NBT.1)

• 1 – Operations & Algebraic Thinking (1.OA.1 – 1.OA.6)

• 1 – Numbers and Operations (1.NBT.1-1NBT.6)

A Moment to Ponder….

Mathematics is reasoning, not memorization. While it is useful to know certain facts and procedures, it is essential that these facts and procedures develop with understanding. Wheatley and Reynolds Coming to Know Number

Students with Number Sense

Have…

• An awareness that numbers

represent relationships

• Good intuition about numbers

• An understanding of magnitude

• An understanding of equivalence

• An awareness of the effect of operations

Reciting number names in order has about the same relation to mathematics that reciting the alphabet has to reading. Evelyn Sharp

SO…… * What does number sense look like

in Kindergarten & first grade?

* What happens in your classroom to

promote development of strong

number sense?

Relationships Among Numbers

Spatial relationships Recognize sets of objects in patterned arrangements and tell how many without counting (subitizing).

Benchmarks of 5 and 10 Develop relationships for numbers

Spatial Relationships • Can you visualize the patterns children are likely

to see on dice, cards, and dominoes?

• Dot Cards can help children: – Recognize sets of objects in patterned arrangements –

tell how many without counting

– Several common patterns for most numbers

– Patterns can be made up of two or more easier patterns of smaller numbers

**After 4 dots, students start to compose and decompose

Let’s Practice!!!!!

Why Use Dot Cards?

• Why?

– Encourage reflective thinking about patterns to construct relationships.

– Naming quantities without counting one by one!

• Why is it important to use a variety of patterned arrangements of dots on the cards?

• What is the role of questioning in these activities?

Benchmarks of 5 and 10 • “Ten frames encourage students to form mental images that

they can use in determining the number in a set without counting: it fosters the development of thinking strategies. As students mentally ‘move’ dots to form familiar patterns, they are developing flexibility of thought and dynamic imagery.

• Transforming images to solve problems is at the heart of doing mathematics. Students may see three blank spaces in one ten frame and move three from another ten frame to make a ten. This ‘making ten’ is most powerful and leads to efficient ways of adding and subtracting.”

Grayson Wheatley

5 and 3 more Two away from 10

Since ten plays such a large role in our numeration system and two fives make up 10, it is very useful to develop relationships for the numbers one to 10 to the important

anchors of five and 10

Game Play • Students take a number card from the deck and put

that number of counters on their 10 frame

• How many counters have you put in the ten frame?

• How many counters are needed to fill the 10 frame? How did you know?

Addition around the World

Children should learn to use the benchmark of ten, doubles, and doubles plus or minus one as strategies.

Everyday Use ten frames as a way to keep track

of the days in school!!!

Ten frames flash. (several mini ten frames)

http://illuminations.nctm.org/ActivityDetail.aspx?ID=75

Place Value

• Time to reflect…

– What do you remember about place value when you were in elementary school? How was it taught?

– Place Value begins in Kindergarten and continues with greater emphasis in first grade? How does this compare to what you learned as a child?

– Why is the K-1 foundation so important????

Place Value Assessment Task Show 18 counters. Ask the child to indicate in the drawing what the 8 means. Ask the child to indicate in the drawing what the 1 means. Ask the child to indicate in the drawing what 18 means.

What understanding does this child have? What understanding is incomplete, not yet developed?

Place Value Task to Check Understanding

• Make 5 sticks of ten

• Add 3 more cubes

• Ask, “How many cubes altogether?”

• Think about your children and number sense.

• Discuss the variety of responses you may get from children.

• What does this tell you and where do you go from here?

Possible Responses

• Counting by ones – “1, 2, 3…52, 53”

• Counting by groups and singles –

– “1, 2, 3, 4, 5 sticks of ten and 1, 2, 3”

• Counting by tens –

– “10, 20, 30, 40, 50, 60, 70 ,80”

• Counting by tens and ones

– “10, 20, 30, 40, 50, 51, 52, 53”

Place Value

• Counting plays a key role in constructing base-ten ideas about quantity and connecting these concepts to symbols and oral names for numbers.

• Children need frequent opportunities to count sets of objects in several ways.

Place Value • Children must integrate the grouping-by-tens

concepts with what they know about number from counting by ones.

– Simply showing children groups of 10 and telling them “ten ones is the same as 1 ten” will not construct the idea for them.

– Seeing 10 ones as both 10 ones and 1 ten is an important first step toward understanding the structure of the base-ten number system.

Components of Place Value

TENS ONES

5 3

Tens Ones

5 tens 3 ones

53

** Groupings by tens ** Standard oral names for numbers ** Written forms of numbers

Components of Place Value

• Grouping by tens – exchange 10 ones for a ten and ten tens for a hundred.

• Realizing the same number can be represented with different but equivalent groupings – Example: 28

– 2 tens and eight ones

– 1 ten and 18 ones

– 28 ones

** All represent the number 28

Components of Place Value

• Standard oral names for numbers – Connect the base-ten language with the standard

oral names for numbers.

– Base-ten language encourages thinking in terms of groups instead of singles

53 5 tens 3 ones fifty-three The teaching of place value needs to be intentional to

connect representations of number, the symbolic form of the number, and the oral language of the number.

Components of Place Value

• Written forms of numbers – Our place value system allows us to represent

numbers with just 10 digits

– Digits have different values depending on their positions in the numbers

The pattern of ones, tens, and hundreds repeated in each period: one thousands, ten thousands, hundred thousands; one millions, ten millions, hundred millions, etc.

Place Value Activities

Ten frames and two-column mats

What are the benefits of using this type of place value mat?

1. Why are different models of place value important? This picture goes from the most concrete to the most abstract? 2. Where do you start? Understanding has to come from the student. If you only use one model, they won’t know what to do when given a different model. 3. Thoughts????????

Student Work

• Look at packet A. Talk about each child’s strategy.

• Order the pages – least sophisticated strategy to most sophisticated.

• Where is each child in their development of number sense???

A Moment To Reflect & Plan

• What is one strategy or practice you plan to add to your classroom to help with developing number sense?

• Can you integrate what you learned today into your math plans?

• THANK YOU and have a great

school year!