What is Numeracy?

1. What is Numeracy?

2. Numeracy is the effective use of mathematics to meet the general demands of life at home, in paid work, and for participation in community and civic life.

3. Numeracy is closely related to mathematics. • The knowledge of mathematical concepts and procedures alone is not enough to guarantee numeracy. • What mathematics is taught and how it is taught has an important bearing on the development of young people’s numeracy.

4. Mathematics is a school subject and classes are timetabled for the teaching of mathematics. • This is not the case for numeracy. • It may therefore be helpful to think of numeracy, as a key outcome of how mathematics is taught and learned – something that is acquired and integrated with what students learn in other school subjects, and in their wider experiences both in and out of school.

5. Teaching numeracy requires teaching through many numerical activities. There is also a place for drill and practice about mental mathematics. For students to become numerate, they must be given opportunities to practice and apply the mathematics they have learned not only in the mathematics lesson, but in other areas of the curriculum

6. The Maths Curriculum is divided into 5 Strands.The first and the biggest Strand is Numbers.

7. These 5 main strands are then further split into sub strands • SUB-STRANDS • 1 Numbers Whole Numbers, Operations, Fractions, Decimals. • 2 Measurement Length & Area, Volume & Capacity, Mass, Time, Money and Temperature. • 3 Geometry/Shapes, Angles and Directions. • 4 Chance/ Data Probability, Data. • 5 Algebra Patterns, Equations.

8. Children learn about numbers very early in their life. • They see numbers all around them. •  Children learn numbers in phases. • There are 6 major phases that children embark on to be able to have a good number sense.

10. The first phase is the Emergent Phase. • In this phase children will recognize the difference between how big and small the amount of physical material that they see and would be able to distinguish between the two.

11. From the Emergent Phase they move into the Matching Phase where children match numbers to objects and number figures they see. • In your classrooms they are given matching exercises as their activities. •  As a result of the matching phase they should be able to relate the words into numbers, number of objects and vice-versa.

12. After the matching phase they move into the Quantifying Phase. • Quantification is the formal name for the concept of figuring out how many things you’ve got. Counting is just one method of quantification

13. From the Quantifying phase children advance into the Partitioning phase. • In this phase children can partition numbers and know the Place Value of each digit. They can divide and place 2 to 3 digit numbers and more in to their different place values.

14. The next phase is the Factoring phase. • In this phase students are able to relate different types of multiplication and division situations involving whole numbers. • Children should be able to apply any of the 4 operations to solve problems. • They know that if you multiply 6 and 2 either way the product is 12.

15. The last phase is the Operating phase. • In this phase, students are expected to read and say any type of number without any difficulty. • They are able to link a fraction to its decimal equivalence, ordering decimals in ascending or descending order, and work out equivalent fractions

16. The next sub strand is OPERATION. • There are four operations in maths that help us to solve problems. • No matter what problem students are trying to solve, one of these four operations - addition, subtraction, division and multiplication - will help them to work it out. They will also need to know how the different operations work as opposites.

17. The first Basic Operations is Addition • Addition also means add / plus /sum and total or bringing two or more numbers (or things) together to make a new total. • The numbers to be added together are called the "Addends":

18. The second Basic Operations – Subtraction • Subtraction also means minus, take away, difference • In taking one number away from another, the remainder is the difference.

19. The third Basic Operations – Multiplication • Multiplication also means times, by, product and multiply. • Multiplication is also repeated addition. • For e.g 6+6+6 (three 6s) make 18: • It can also be said that 3+3+3+3+3+3 (six 3s) make 18 •  But we can also multiply by fractions or decimals, which go beyond the simple idea of repeated addition: • Example: 3.5 × 5 = 17.5 • which is 3.5 lots of 5, or 5 lots of 3.5

20. Division also means divide, goes into ...is splitting into equal parts or groups. • Division has its own special words to remember. • Let's take the simple question of dividing 22 by 5. The answer is 4, with 2 left over. Here we see the important words:

21. A Fraction is ... • ... part of a whole. • A fraction is written with the bottom part (the denominator) telling us how many parts the whole is divided into, and the top part (the numerator) telling us how many parts we have.

22. A Decimal Number is ... • ... a number that contains a Decimal Point. • The value of the number moving towards the right from the point is 10 times smaller than the number to its left. • The value of the number moving towards the left from the decimal point is 10 times bigger than the number to its right. 17 . 591 • 1 Tens • 7 Units • 5 tenths or 1/10 • 9 hundredths or 1/100 • 1 thousandths or 1/1000

23. Strategy on Fractions • Teachers will need prepare some long strips of paper, paper lips or clothes pegs and paper cutouts. • Children are to write simple fractions on the cutouts and peg up their fractions on the long strip of paper. • This activity will help children locate the fractions on a line/ list the fractions in ascending or descending order/ equivalent fractions.

24. The next Strand is Measurement. • Measurement is an important application of mathematics that students will need for independent living and for many kinds of employment. As well as measuring, the ability to estimate is an important skill that students must possess

25. Measurement is finding a number that shows the dimension or quantity of an object. • There are measuring instruments that can be used to help students in measuring. • Children are to be taught how to use the measuring instruments correctly.

26. There are six sub – strands in Measurement ; • length and area /volume and capacity / mass / time/ money and temperature. • Length – relates to how long an object is where students can measure using the standard measuring units or arbitrary units, like paper clips etc laid alongside the object to be measured. slides • Area - is the amount of space within a boundary where the area is determined by counting the square grids or by multiplying the length and the width of the shape.

27. Volume – is associated with solid 3- dimensional objects and could be introduced using Diennes Blocks. • Capacity – is related to liquids and Capacity can be measured using a measuring cylinder. • Mass –The mass of an object is the amount of matter which it contains and the weight is the force of the gravitational pull of the earth . • The weight changes depending on where the object is. An object will weigh more at sea level than at the top of mountains and it will be weightless in outer space. • Time – is the awareness of the changes to the events that happen around us. It can be measured by observing and comparing the regularity of such changes using clocks, watches and calendars. • Money – a topic that is understood by children because of its regular use in their daily lives. It is the other application which students have difficulties in. • Temperature - is related to how hot or cold an object is. Accurate measurement is taken using a thermometer.

28. Estimation is an important component of measurement. • It is a skill that students must learn to possess since they will not be using the measuring tools all the time.

29. Geometry • Children live in a world that is full of shapes. They are surrounded by different types of shapes. • Geometry is the study of shapes. It involves representation of shape, size, pattern, position and movement of objects in the three-dimensional world, or in the mind of the learner

30. In the primary curriculum students learn to recognize, visualize and draw shapes, describe the features and properties of two-dimensional and three- dimensional objects in static and dynamic situations.

31. Two-dimensional shapes and three-dimensional figures have properties that allow them to be identified, compared, sorted, and classified. • Experience with two-dimensional shapes and three-dimensional figures, represented in a variety of forms and sizes, allows students to understand those properties.

32. Angles and Lines - Students get to learn more about the different types of angles and lines. •  There are five different types of angles; • 1. Acute angle • 2. Right angle • 3. Obtuse angle • 4. Straight angle • 5. Reflex angle •  There are five different types of lines; • 1. line • 2. line segment • 3. ray • 4. parallel lines • 5. perpendicular lines.

33. Chance and Data •  In this Strand students get to learn about Probability and Data. • In the real world, events can not be predicted with total certainty. The best we can do is say how likely they are to happen, using the idea of probability. • The Probability of an event happening • = Number of ways it can happen. • Total number of outcomes • The Probability will always be less than 1.

34. Probability can be shown on a Probability Line

35. The line begins from zero and ends at one. • So the probability of an event occurring is either impossible, unlikely, even chance likely and certain.

36. Data • Data is a collection of facts, such as numbers, words, measurements, observations or even just description of something. • Data can be qualitative or quantitative. • Qualitative data is descriptive information (it describes something) Quantitative data, is numerical information (numbers).

38. Quantitative data can also be • Discrete or Continuous. • Discrete data can only take certain values (like whole numbers) • Continuous data can take any value (within a range) • Put simply: Discrete data is counted, Continuous data is measured

39. Example: What do we know about Arrow the Dog? • Qualitative: • He is brown and black • He has long hair • He has lots of energy • Quantitative: • Discrete: • He has 4 legs • He has 2 brothers • Continuous: • He weighs 25.5 kg • He is 565 mm tall

40. DATA is collected from • polls surveys observations questionnaires / interviews examining past records experimentation using instruments • After DATA collection the results are shown on; • bar graphs • circle graphs • picture graphs • line graphs • frequency distributions • histograms.

41. Algebra • Equations • Equations are mathematical expression (sentence) where there is an equal sign (=) to indicate what is on the left equals to what is on the right. The missing numbers are called the variables. The variable has a value and the equation has to be solved to determine its value. Solving may involve one or two operations.

42. For e.g. in this equation; • 4a + 7 = 19 • The parts are • 4 - Coefficient • a - Variable • + - Operator • 7 & 19 - Constants

43. Patterns • Patterns are an important element in Mathematics and are used extensively. Patterns are usually thought of as a design or elements which are created by repetition. • Number patterns are clearly seen in multiplication tables.