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At Last, A Comprehensive Guide to Help Your Students Develop Good Number Sense

I have put this guide together to assist you with understanding what number sense is as well as list strategies and activities you can implement in your class to develop number sense in your students.  Specifically, the article outlines:

  • What is number sense;
  • How you would recognise students that have good or poor number sense;
  • Ways you can help your students develop number sense; and
  • Activities you can use in your class to develop number sense.

What is Number Sense?

Children who have good number sense are able to use and understand an array of numerical strategies and concepts in conjunction with the ability to use these skills in a number of different ways, such as in different contexts.  In other words, number sense involves the ability to use numbers and processes in flexible ways (2).

In order for children to develop good number sense they require a range of specific skills.  These skills include:

  • Flexibility;
  • Estimation;
  • Awareness of relationships;
  • Patterns and links;
  • Determining the reasonableness of results;
  • Prediction;
  • Mental computation; and
  • Reflection (1).

How Would You Recognise a Student in Your Class With Good Number Sense?

Students in your class that have good number sense would demonstrate most of the following characteristics:

  • Use mental computation (determining an answer to a calculation or problem in one’s head), rather than relying solely on paper and pencil or a calculator (5).
  • Possess a number of different ways that they could select from for completing calculations (4).
  • The ability to select an appropriate strategy for solving a calculation or problem (4).
  • Be able to check answers via a number of different strategies, such as with a calculator, paper and pencil or with mental computation (4).
  • Use estimates to gain a rough idea of an answer and know when estimating is effective (2).
  • Generally possess a feeling of competence and comfort with numbers in a variety of contexts (1).
  • The ability to make sense of varied number situations (2).
  • Determine reasonableness of answers and results (2).
  • Know of the relationships that can occur between numbers, such as with the four operations of addition, subtraction, multiplication and division and how individual numbers can relate to others in a variety of ways (1).

How Would You Recognise a Student in Your Class With Poor Number Sense?

Students in your class that have poor number sense would demonstrate the following characteristics:

  • Rely heavily on paper and pencil and calculators for performing simple calculations in varied situations, such as determining half price of an item in a shop or using a standard algorithm for a calculation that could be completed mentally (4).
  • Does not check to see if the answer obtained would be reasonable, or in other words if it is a realistic possibility (2).
  • Does not use estimation prior to completing a calculation, therefore does not have an idea of whether or not the answer obtained would be logical.
  • May have a limited number of strategies to select from that can be used to solve problems or complete calculations.  This could lead to the selection of an inappropriate strategy for the situation.
  • Portray a negative attitude towards mathematics and generally have a feeling of unease.
  • Unsure of how numbers can relate to one another.  For example does not use subtraction and addition or multiplication and division interchangeably.

5 Ways You Can Help Your Students Develop Number Sense

1. Provide many opportunities for your students to make estimations prior to completing a calculation.  Opportunities to estimate should also be provided in varied situations.  For example: estimate the cost of a number of items from the shop to determine if the person has ample money, or estimate how long it would take to reach a destination if travelling at a particular speed (4).

2. Before your students complete calculations with the aid of pen and paper or calculators allow them to use mental computation.  Provide opportunities for students to discuss how they found an answer and what they actually did in their head.  Emphasise the relationships between numbers that students used.  For instance discuss how students found an answer for the calculation of 86+57.  Some students may have added 80+50 first and then added 6+7 to find an answer, or other students may have found an answer in an entirely different way (4).

3. Provide many opportunities that connect mathematics to the real world, inside and outside the classroom.  This could be achieved in a number of ways, such as: when collecting money for excursions ask students how much change they may require, or when going on an excursion discuss how many buses may be required to transport all the students and teachers (3).

4. Students should be exposed to many different strategies that they can then select from to solve a problem or determine an answer to a calculation.  This could also include knowing which strategy would be best suited for a particular situation.  For example: when is it okay to estimate and when is accuracy required (3).

5. Make available many opportunities for students to discuss the different ways they use to compute in varied situations.  Encourage students to explain their reasoning out loud so that other students are exposed to many different ways.  For example how many different ways they could add two numbers, or the different ways that people determine the football scores (6 goals, 5 behinds, how many points scored altogether?) (3).

The abovementioned activities are effective as they:

  • Promote mental computation;
  • Encourage students to use a variety of methods and strategies for solving problems and completing calculations;
  • Relates students’ learning experiences to the ‘real world’ and prior knowledge;
  • Encourages the use of estimation as a form of checking if answers obtained are reasonable; and
  • Promote discussion and reflection of strategies used.  Students become exposed to many different ways that problems and calculations could be solved.

2 Activities for Developing Number Sense in Your Classroom

Activity One: Today’s Target

(5)

Today’s target is__________

Try to make today’s target in each of these ways.

  1. Adding two numbers
  2. Finding the difference of two numbers
  3. Multiplying two numbers
  4. Dividing one number by another
  5. Adding three numbers
  6. Multiplying three numbers
  7. Multiplying and subtracting
  8. Using a fraction
  9. Using a decimal
  10. Doing it an unusual way.
  • Teacher and students select the target number.
  • Ask for examples for each of the restrictions from the students.
  • Allow students to complete individually.

How This Activity Could Be Used With Your Students

This activity could easily be adapted to suit any year level, for example modify or do not use the series of questions.  If the basic activity were left as is, it would be useful for a year five or six class.  The following table depicts the series of lessons that could be used leading up to the ‘Today’s target’ lesson.

Lessons Description Purposes
One
  • Provide students with a number.
  • Ask them to find out possibilities of what the question could be for this answer.
  • Document these on the board.
  • Categorise the responses into addition, subtraction, multiplication and division.
  • This is the ‘tuning in’ activity the teacher could use.
  • It demonstrates to the teacher at what level of number sense individual students are operating.
  • Doesn’t provide any limits to the students so they can be as creative as they like.
Two
  • Provide students with an A4/A3 sheet of paper.
  • The number appears in the middle.
  • The paper is divided into quarters with an operation in each quarter (addition, subtraction, division, multiplication).
  • Students determine the questions for the answer in the middle of the sheet, using the operation in each quarter of the page.
  • Focuses on the four operations.
  • Teacher can determine those students that may be having difficulties with some of the operations.
  • Still provides the opportunity for creativity.
Three
  • ‘Today’s Target’ lesson.
  • Do not use as a worksheet complete the activity orally (provide the questions on an overhead).
  • Allow students to discuss the possibilities and encourage them to explain their responses.
  • Encourage students to complete the activity mentally, rather than using pen and paper or calculators.  These can be added at a later stage if necessary.
  • More specific questions focusing on the four operations.
  • Encouraging students to consider other possibilities, such as fractions and decimals.
  • Again directs teacher to the students that may need extra work and the ‘problem’ areas.

How This Activity Develops Number Sense

  • Promotes the use of mental computation;
  • Students reflect and discuss on the strategies used;
  • Students experience different ways in which numbers and calculations can be represented;
  • Students draw on their existing knowledge of numbers, processes and operations;
  • Students will become aware of the patterns and relationships of numbers and the many ways that these can be represented; and
  • Students begin to make generalisations about the patterns that they are encountering.

Activity Two: Think Board

  • A number is selected to place in the middle of the think board, either teacher or student selected
  • The students represent their understanding of the number in the centre by completing each quarter: a written story of the number, a picture depicting the number, represent the number with symbols and a model of concrete/real items representing the number
  • Activity can be extended by placing a calculation, fraction, decimal etc. in the centre of the board

How This Activity Develops Number Sense

  • Students are connecting what they know about numbers to the real world;
  • Students are experiencing different ways in which numbers can be represented (e.g. with symbols, real things, in a story etc);
  • Students discuss their boards and reflect on the way that they have represented the information; and
  • Students are using many different strategies to represent numbers in flexible ways.

I hope this guide has helped to provide you with some ideas of how you can develop good number sense in your students.  If you have any questions or comments please leave them below.

References

1. Anghileri, J. (2000). Teaching number sense. London: Continuum.

2. Bobis, J., Mulligan, J., Lowrie, T., & Taplin, M. (1999). Mathematics for children: Challenging children to think mathematically. New South Wales: Prentice Hall Australia Pty Ltd.

3. Burns, M. (1998). Can I balance arithmetic instruction with real-life math? Instructor, April, 55-58.

4. McIntosh, A. (1996). Number sense. Journal of Education, Tasmania, Winter, 18-19.

5. McIntosh, A., Reys, B., Reys, R., & Hope, J. (1997). Number sense: Simple effective number sense experiences. California: Dale Seymour Publications.

6. Sowder, J. (1990). Mental computation and number sense. Arithmetic Teacher, 37(7), 18-20.

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5 Responses to At Last, A Comprehensive Guide to Help Your Students Develop Good Number Sense

    • Hi, thanks for stopping by and leaving a comment on my blog :-). Yes I also agree it is hard work putting something like this together! If you keep persisting, I’m sure you’ll get there!

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