Chapter 8 Developing Early Number Concepts and Number

Big Ideas 1. Counting tells how many things are in a set. 1. Numbers are related to each other through a variety of number relationships. 2. Number concepts are intimately tied to the world around us. Copyright © 2015 Pearson Canada Inc. 2

Early Number Development Is Related to Other Mathematics Curriculum Content for the development of number n Operations (Chapter 9) n Measurement (Chapter 19) n Data (Chapter 21) Content affected by how well early number concepts have been developed n Basic Facts (Chapter 10) n Place Value and Computation (Chapters 11 and 12) Copyright © 2015 Pearson Canada Inc. 3

Research-Based Recommendations for High-Quality Learning Activities for Ages 3– 6 1. 2. 3. 4. 5. 6. Enhance children’s natural interest in mathematics Build on children’s experience and knowledge Base mathematics curriculum and teaching practices on knowledge of young children’s development Use formal and informal experiences to strengthen children’s problem-solving and reasoning processes Provide opportunities for children to explain their thinking as they interact with the mathematics Thoughtfully and continually assess children’s mathematical knowledge, skills, and strategies Copyright © 2015 Pearson Canada Inc. 4

Number Concepts: Quantity, Counting, and Knowing How Many § Quantity and the Ability to Subitize § Early Counting § The Development of Verbal Counting Skills § Meaning Attached to Counting Objects § Thinking about Zero § Numeral Writing and Recognition § Counting On and Counting Back Copyright © 2015 Pearson Canada Inc. 5

Quantity and the Ability to Subitize Copyright © 2015 Pearson Canada Inc. 6

Early Counting the sequence of number words is rote. n The meaning attached to the counting is the key conceptual idea n Children will learn how to count before they understand that the last count word indicates the amount of the set or the set’s cardinality. Copyright © 2015 Pearson Canada Inc. 7

Each number includes those that came before. Copyright © 2015 Pearson Canada Inc. 8

Early Counting Copyright © 2015 Pearson Canada Inc. 9

Formative Assessment: Try This One Show a card with five to nine dots in a row: How many dots are on the card? Children that respond with the correct number have made the connection to the cardinality principle. Please get the same number of counters as there are dots on the card. (For indicators, see next slide. ) Copyright © 2015 Pearson Canada Inc. 10

Sequence of Indicators n These are in order from a child that does not attach meaning to the count to one who is using counting as a tool. n n n Does the child not count, but instead make a similar pattern with the counters? Will the child recount? Does the child place the counters in a one-to-one correspondence with the dots? Or does the child count the dots and retrieve the correct number of counters? Is the child confident that there is the same number of counters as dots? Copyright © 2015 Pearson Canada Inc. 11

Numeral Writing and Recognition Reading and writing numerals is similar to teaching them to read and write letters of the alphabet. Engaging ways: n Make numerals with clay n Trace in shaving cream n Write in the air Calculator keypad is good instructional tool. Copyright © 2015 Pearson Canada Inc. 12

Counting On and Counting Back Copyright © 2015 Pearson Canada Inc. 13

Comparing Sets n n n More than Less than Equal to Children need to construct sets using counters and make comparisons or choices between two or more sets. Which is more (greater than)? Which is less (less than)? Which is same (equal to)? 14 Copyright © 2015 Pearson Canada Inc.

Early Number Sense Number sense goes beyond learning counting skills or memorizing facts and applying algorithms. “Number sense refers to a general understanding of number and operations as well as the ability to apply this understanding in flexible ways to make mathematical judgements and to develop useful strategies for solving problems” (Ontario Ministry of Education, 2005, p. 8) Copyright © 2015 Pearson Canada Inc. 15

Early Number Sense cont. “Number sense develops when students connect numbers to real-life experiences, and use benchmarks and referents. This results in students who are computationally fluent, flexible with numbers, and have intuition about numbers. The evolving number sense typically comes as a by-product of learning rather than through direct instruction. However, number sense can be developed by providing rich mathematical tasks that allow students to make connections. (Alberta Education, 2006, p. 11) Copyright © 2015 Pearson Canada Inc. 16

Number Relationships 1– 10 n n n One more and two more, one and two less Anchors or benchmarks of 5 and 10 Part-part-whole relationships Children initially construct these relationships with counting. Copyright © 2015 Pearson Canada Inc. 17

Crazy, Mixed-Up Numbers: Try This One Construct the number you see below. Tell the children not to clear their ten-frame between the number callouts. How many counters need to be added or removed to make eight? Copyright © 2015 Pearson Canada Inc. 18

Part-Whole Copyright © 2015 Pearson Canada Inc. 19

Missing-Part Activities Copyright © 2015 Pearson Canada Inc. 20

Dot Cards as a Model for Teaching Number Relationships Copyright © 2015 Pearson Canada

Number Relationships 10– 20 n A set of ten plays a major role in the understanding of numbers 10– 20. n n n Children do not see a numeric pattern in the numbers 10– 20. Suggest to students that they think of 10 as a bundle of 10 ones, called a ten. Think of the teens as a ten and some more ones. Copyright © 2015 Pearson Canada Inc. 22

Number Sense in Their World Estimation and measurement Try This One Cut out a large footprint 18 inches long. Ask children to tell you about how many it will take to measure the rug in the classroom. The crucial word is about and the key is guiding children to understand that it does not require a specific number. Copyright © 2015 Pearson Canada Inc. 23

Estimation and Measurement One of the best ways for students to think of real quantities is to associate numbers with measures of things (length, mass (weight), and time etc. ) Copyright © 2015 Pearson Canada Inc. 24

Data Collection and Analysis n n Encourage children to generate ideas for what data to gather. Use the graphed data to compare number relationships rather than only referencing more and less. More students brought apples for snack than bananas. Three fewer people brought oranges than brought apples. Copyright © 2015 Pearson Canada Inc. 25

Classroom Routines Find ways to weave rich mathematics into regular routines such as circle time, attendance, calendar, lining up, cleaning up, story time, and other classroom routines. e. g. Choose a number of the day. If today’s number is 4, ask “What do we know about the number 4? ” Answers such as “I am four years old. ” “My dog has 4 legs” and “There is a 4 in my house number” help children connect numbers to their lives. Copyright © 2015 Pearson Canada Inc. 26

Literature Connections Children’s literature abounds with wonderful counting books and visually stimulating number-related books. Examples: Ten Little Hot Dogs (Himmelman, 2010) Two Ways to Count to Ten (Dee, 1988) Anno’s Counting (House Anno, 1082) Can you think of others? Copyright © 2015 Pearson Canada Inc. 27