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## Helping Children Develop Number Sense

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**Helping Children Develop Number Sense**Dr. Laura McLaughlin Taddei**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. Learning Outcomes**What are the big ideas of number sense (Van de Walle, Lovin,**Karp, & Bay-Williams, p. 100, 2014)? Big Ideas of Number Sense**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 Four Aspects of Early Numeracy**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 Teaching Number Sequence**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? Practice**What are some ways to accomplish this goal?**• Taking attendance • Daily calendar • Others? Ways to Teach Number Sense with Daily Routines**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 Learning Trajectory for Counting**Videos –**• Mouse Collection – Story telling and math • Number Arrangements Video • On Blackboard • Reflections • Strategies you would use**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 Practice**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 What is Number Sense?**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 Relationships involving small numbers**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 Practice**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 Children understanding 10**Choose an activity on pages 118 to 120, create the activity,**demonstrate the activity, discuss the activity – modifications/extensions. Practice**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 Kindergarten Children**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**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 Applying Numbers to the Real World**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 Resources