Helping Children Develop Number SenseDr. Laura McLaughlin Taddei

Learning Outcomes

• Learning Goal: Students will develop and present various examples of developmentally appropriate math experiences for young children.

• Learning Goal: Students will develop, implement, assess, and modify curriculum and lessons for children from Pre-K through 4th grade using PA state standards and National standards if applicable.

• Learning Goal: Students will plan, implement, and adapt for all children appropriate developmental, cultural, and linguistic instructional practices and strategies.

Big Ideas of Number Sense

• What are the big ideas of number sense (Van de Walle, Lovin, Karp, & Bay-Williams, p. 100, 2014)?

Four Aspects of Early Numeracy

• We want to help children develop the following:• Number sense – the names and the ordered list of number

words• One-to-One correspondence – counting objects by saying

number words in a one-to-one correspondence with the objects

• Cardinality – the last number said when counting tells how many objects have been counted

• Subitizing – quickly recognizing numbers in small groups without counting

Teaching Number Sequence

• Map 11 to 10 and 1• Map 12 to 10 and 2• Use a vertical number line to show how numbers change

when it goes to double digits – see figure 8.1• Provide children opportunities to count backwards and

forwards

Practice

• Group Activity – Find the standards that relate to the games on page 102-103, write the game directions and description on an index card, create the game, adapt the game for diversity/accommodations, have the class participate in the game, discuss the game and ways to modify and/or extend and how will you assess:• Group 1 – Counting Up and Back• Group 2 – Line them up• Group 3 – Fill the towers• Group 4 – How many are there?

Ways to Teach Number Sense with Daily Routines

• What are some ways to accomplish this goal?• Taking attendance• Daily calendar• Others?

Learning Trajectory for Counting

• Emergent Counter – child is unable to count the collection of objects – child may be able to coordinate one number word with one object when counting or may know the correct number sequence

• Perceptual Counter - can count the collection of objects only if objects can be seen

• Figurative Counter – can count the collection of objects even if they are hidden from view – starts counting from 1

• Counting-on counter – child who can start counting from a given number other than 1 and does not need to see objects to count

• Non count-by-ones counter – a child who does not use counting by ones but partitions and combines numbers involved is a non count-by-ones counter – 7 is 3 from 10

• Videos – • Mouse Collection – Story telling and math• Number Arrangements Video• On Blackboard• Reflections• Strategies you would use

Practice

• Group Activity – Find the standards that relate to the games on pages 104-106, write the game directions and description on an index card, create the game, adapt the game for diversity/accommodations, have the class participate in the game, discuss the game and ways to modify and/or extend and how will you assess:• Group 1 – Counting on with counters• Group 2 – Real counting on• Group 3 – Make sets of more or less• Group 4 – Find the same amount

What is Number Sense?

• Grows over time• Results from children exploring numbers, relating them

to real life, and visualizing numbers in different contexts• Teachers need to provide children with opportunities to

continue to understand numbers before jumping into addition and subtraction

Relationships involving small numbers

• Spatial relationships – recognize patterns without counting

• One and two more, one and two less • Anchors or benchmarks of 5 and 10 – develop

relationships for 1 to 10 with the anchors of 5 and 10• Part-part-whole – a number is made up of two or more

parts – 7 can be thought of as a set of 4 and a set of 3

Practice

• Group Activity – Choose one game for the section your group is assigned (pages 107 – 115). Find the standards that relate to the game, write the game directions and description on an index card, create the game, adapt the game for diversity/accommodations, have the class participate in the game, discuss the game and ways to modify and/or extend and how will you assess:• Group 1 – Spatial Relationships• Group 2 – One and two more, one and two less• Group 3 – Anchors or benchmarks of 5 and 10• Group 4 – Part-part-whole relationship

Children understanding 10

• An initial concept of 10 – understands ten as ten ones and does not see 10 as a unit – counts by ones

• An intermediate concept of 10 – child understands 10 as a unit composed of ten ones but relies on materials or representations to help complete tasks involving tens

• A facile concept of ten – child can solve tasks involving tens and ones without using materials or representations – mentally think about two-digit numbers as groups of tens and ones

Practice

• Choose an activity on pages 118 to 120, create the activity, demonstrate the activity, discuss the activity – modifications/extensions.

Kindergarten Children

• Are expected to count to 100 by the end of the school year

• Early exposures to numbers to 100 is important even in kindergarten

• They can learn about the sequence of numbers to 100• Children need to become familiar with counting patterns

to 100

• 100 Chart• Activity 8.24 – work in pairs and identify the patterns in

the 100 chart. • What would be the benefit of doing this?• How about the missing number activity – 8.25

Applying Numbers to the Real World

• Calendar Activities – doing the calendar is not a substitute for teaching mathematics. Why do you think?

• Estimation and Measurement – associate numbers with measures of real things• Have children produce an estimate – this is difficult for young children • The key word to use is “about”

Spend a lot of time on this concept of “about”• More or less than • Closer to or • About• Estimate several things in succession using the same unit• Using a string – measuring things around• Discuss 8.26 and 8.27 and Figure 8.19

Resources

Van de Walle, J., Lovin, L., Karp, K., Bay-Williams, J. (2014). Teaching student-centered

mathematics. Second edition. Pearson Education.

Smith, S. (2013). Early childhood mathematics. Pearson Education