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# International Curriculum

### If you believe that multiplication involves more than memorising answers, then we are with you!

No matter the variances in international curriculums, the BIG PICTURE is the same. Learning multiplication facts cannot be done in isolation or simply by remembering answers. Conceptual understanding, strategy development, number sense and relating to division, are just as important as knowing the answers.

Teaching and learning about multiplication in a meaningful way, is an important endeavour and well worth the time and effort. This is often harder and more challenging than simply encouraging children to memorise their times tables. Delving into concepts and strategies shines a light on student’s number skills and number sense, often revealing deficiencies in other areas of number….and that is exactly why it’s so important!

To set students up for success and continued development in maths, multiplication facts and concepts need to be totally secure. Let’s set about the challenging and rewarding work that needs to be done!

Below are examples of how Mfacts121 links to curriculum around the world. It’s teachers themselves who make the biggest difference to student learning and Mfacts121 can easily be integrated into YOUR classroom or school program!

##### USA: Common Core:

The Common Core refers to ‘addressing the problem of a curriculum that is “a mile wide and an inch deep.”’ ‘…by not only stressing conceptual understanding of key ideas, but also by continually returning to organizing principles such as place value and the laws of arithmetic to structure those ideas.”

For example:

Year 2:

• Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Year 3:

• Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
• Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.Multiply and divide within 100.
• Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Year 4:

• Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
• Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Year 5:

• Fluently multiply multi-digit whole numbers using the standard algorithm.
• Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
##### Australian Curriculum:
Year 3

• Investigate the conditions required for a number to be odd or even and identify odd and even numbers.
• Recall multiplication facts of two, three, five and ten and related division facts.
• Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies.

Year 4:

• Recall multiplication facts up to 10 x 10 and related division facts.
• Investigate number sequences involving multiples of 3, 4, 6 , 7 , 8 , a n d 9 .
• Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder.

Year 5:

• Identify and describe factors and multiples of whole numbers.
• Solve problems involving multiplication of large numbers by one­ or two­-digit numbers using efficient mental, written strategies and appropriate digital technologies.
• Solve problems involving division by a one digit number, including those that result in a remainder.
• Use efficient mental and written strategies and apply appropriate digital technologies to solve problems.

Year 6:

• Identify and describe properties of prime, composite, square and triangular numbers.
• Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers.
##### New Zealand:
End of Year 5:

Number and algebra

In contexts that require them to solve problems or model situations, students will be able to:

• apply additive and simple multiplicative strategies and knowledge of symmetry to:
• combine or partition whole numbers
• find fractions of sets, shapes, and quantities
• create, continue, and predict further members of sequential patterns with two variables
• describe spatial and number patterns, using rules that involve spatial features, repeated addition or subtraction, and simple multiplication.

During this school year, ‘number’ should be the focus of 50–70 percent of mathematics teaching time.

End of Year 6:

Number and algebra

In contexts that require them to solve problems or model situations, students will be able to:

• apply additive and simple multiplicative strategies flexibly to:
• combine or partition whole numbers, including performing mixed operations and using addition and subtraction as inverse operations
• find fractions of sets, shapes, and quantities
• determine members of sequential patterns, given their ordinal positions
• describe spatial and number patterns, using:
• tables and graphs
• rules that involve spatial features, repeated addition or subtraction, and simple multiplication.

During this school year, ‘number’ should be the focus of 50–70 percent of mathematics teaching time.

End of Year 7:

Number and algebra

In contexts that require them to solve problems or model situations, students will be able to:

• apply additive and multiplicative strategies flexibly to whole numbers, ratios, and equivalent fractions (including percentages)

During this school year, ‘number’ should be the focus of 40–60 percent of mathematics teaching time.

##### United Kingdom:
Year 2 programme of study

Number – multiplication and division

Pupils should be taught to:

• recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers
• calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs
• show that multiplication of 2 numbers can be done in any order (commutative) and division of 1 number by another cannot
• solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts

Year 3 programme of study

Number – multiplication and division

Pupils should be taught to:

• recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
• write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods
• solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects

Year 4 programme of study

Pupils should be taught to:

• recall multiplication and division facts for multiplication tables up to 12 × 12
• use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together 3 numbers
• recognise and use factor pairs and commutativity in mental calculations
• multiply two-digit and three-digit numbers by a one-digit number using formal written layout
• solve problems involving multiplying and adding, including using the distributive law to multiply two-digit numbers by 1 digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects

Year 5 programme of study

Pupils should be taught to:

• identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbers
• know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
• establish whether a number up to 100 is prime and recall prime numbers up to 19
• multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers
• multiply and divide numbers mentally, drawing upon known facts
• divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context
• multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000
• recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)
• solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes
• solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
• solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates