Creative Mathematics
A creative approach to Math will set the stage for a long and successful approach to Mathematics. These are some of the basic principles of the curriculum:
Problem solving
* Approach problems involving number, and data presented in a variety of forms,
in order to identify what they need to do
* Develop flexible approaches to problem solving and look for ways to overcome difficulties
* Make decisions about which operations and problem-solving strategies to use
* Organize and check their work
Communicating
* Use the correct language, symbols and vocabulary associated with number and
data
* Communicate in spoken, pictorial and written form, at first using informal language and recording, then mathematical language and symbols
Reasoning
* Present results in an organized way
* Understand a general statement and investigate whether particular cases match it
* Explain their methods and reasoning when solving problems involving
number and data.
Numbers and the number system
Count reliably up to 20 objects at first and recognize that if the objects are
rearranged the number stays the same; be familiar with the numbers 11 to 20;
gradually extend counting to 100 and beyond
Number patterns and sequences
* Create and describe number patterns; explore and record patterns related to
addition and subtraction, and then patterns of multiples of 2, 5 and 10
explaining the patterns and using them to make predictions; recognize sequences,
including odd and even numbers to 30 then beyond; recognize the relationship
between halving and doubling
The number system
Read and write numbers to 20 at first and then to 100 or beyond; understand and
use the vocabulary of comparing and ordering these numbers; recognize that the
position of a digit gives its value and know what each digit represents,
including zero as a place-holder; order a set of one- and two-digit numbers and
position them on a number line and hundred-square; round any two-digit number to
the nearest 10.
Calculations
* Understand addition and use related vocabulary; recognize that addition can be done in any order; understand subtraction as both 'take away' and 'difference' and use the related vocabulary; recognize that subtraction is the inverse of addition; give the subtraction corresponding to an addition and vice versa; use the symbol '=' to represent equality; solve simple missing number problems [for example, 6 = 2 + ]
* Understand multiplication as repeated addition; understand that halving is the inverse of doubling and find one half and one quarter of shapes and small numbers of objects; begin to understand division as grouping (repeated subtraction); use vocabulary associated with multiplication and division
* Develop rapid recall of number facts: know addition and subtraction facts to 10 and use these to derive facts with totals to 20, know multiplication facts for the 2 and 10 multiplication tables and derive corresponding division facts, know doubles of numbers to 10 and halves of even numbers to 20
* Develop a range of mental methods for finding, from known facts, those that they cannot recall, including adding 10 to any single-digit number, then adding and subtracting a multiple of 10 to or from a two-digit number; develop a variety of methods for adding and subtracting, including making use of the facts that addition can be done in any order and that subtraction is the inverse of addition
* Carry out simple calculations of the form 40 + 30 = , 40 + = 100, 56 - =
10; record calculations in a number sentence, using the symbols +, -, , and =
correctly [for example, 7 + 2 = 9].
Solving numerical problems
* Choose sensible calculation methods to solve whole-number problems (including problems involving money or measures), drawing on their understanding of the operations
* Check that their answers are reasonable and explain their methods or
reasoning.
Processing, representing and interpreting data
* Solve a relevant problem by using simple lists, tables and charts to sort, classify and organize information
* Discuss what they have done and explain their results.
Principles
* During the primary stage, pupils should explore knowledge, skills and
understanding of numbers through:
* Practical activity, exploration and discussion
* Using mathematical ideas in practical activities, then recording these using objects, pictures, diagrams, words, numbers and symbols
* Using mental images of numbers and their relationships to support the development of mental calculation strategies
* Estimating, drawing and measuring in a range of practical contexts
* Drawing inferences from data in practical activities
* Exploring and using a variety of resources and materials
* Activities that encourage them to make connections between number work and
other aspects of their work in mathematics.