Make Sense of Numbers to Solve Problems

• solve addition and subtraction problems by counting all of the objects.

• solve multiplication problems by counting all the objects.

• the sequence of numbers, forwards and backwards, to at least 20.

• addition facts with sums of 5 or 10 and the decade facts.

• solve addition and subtraction problems by counting on or counting back, using ones and tens.

• solve multiplication problems by skip-counting, often in conjunction with one-to-one counting and often keeping track of the repeated counts by using materials (for example, fingers) or mental images.

• find a fraction of a set by using equal sharing.

• the sequence of numbers, forwards and backwards, to at least 100
• how to skip-count in twos, fives and tens to 100.

• 10 as a counting unit, the tens in numbers to 100 and the place values of digits in whole numbers up to 100.

• basic addition and subtraction facts up to 10 + 10.

• solve two-digit by one-digit addition and subtraction problems mentally, using partitioning strategies.

• solve single-digit multiplication and division problems mentally, using known multiplication facts and repeated addition.

• the sequence of numbers, forwards and backwards, to at least 1,000
• the number that is 1, 10 and 100 before or after a given number in the range 0–1,000
• how to skip-count in twos, threes, fives and tens to 1,000
• how to order fractions with like denominators.

• the tens and hundreds in numbers to 1,000 and the place values of digits in whole numbers up to 1,000.

• basic multiplication and division facts up to 10 x 10.

• solve multi-digit addition and subtraction problems, using partitioning strategies

or alternatively

• justify the reasonableness of answers to problems solved, using a calculator or algorithm.

• solve multiplication and division problems with single digit multipliers or divisors mentally, using partitioning strategies and deriving from known multiplication facts.

• use known multiplication and division facts to find fractions of a whole number.

• the sequence of numbers, forwards and backwards, by ones, tens, hundreds and thousands, to a million
• how to give the number 1, 10, 100 or 1,000 before or after a given number in the range 0–1,000,000
• the sequence of decimal numbers in tenths and hundredths
• how to order unit fractions.

• how many tens, hundreds and thousands
  there are in any whole number
• that 10 tenths make one whole.

• basic multiplication facts with tens,
  hundreds and thousands
• fraction and decimal groupings that
  make 1.

• solve addition and subtraction problems involving decimals and integers, using partitioning strategies

or alternatively

• justify the reasonableness of answers to problems solved, using a calculator or algorithm.

• solve multiplication or division problems with multidigit whole numbers, using partitioning strategies

or alternatively

• justify the reasonableness of answers to problems solved, using a calculator or algorithm.

• use multiplication and division strategies to solve problems that involve simple equivalent fractions and simple conversions between fractions, decimals and percentages.

• the sequences of integers, fractions, decimals and percentages, forwards and backwards, from any given number.

• how many tenths, hundredths and thousandths are in any number, including decimal numbers
• how to convert percentages to decimals and vice versa
• what happens when a whole number or decimal is multiplied or divided by a power of 10.

• common factors of numbers up to 100
• fraction, decimal and percentage conversions for halves, thirds, quarters, fifths and tenths
• the convention for exponents.

• solve addition and subtraction problems involving fractions, using partitioning strategies

or alternatively

• justify the reasonableness of answers to problems solved, using a calculator or algorithm.

• solve multiplication or division problems with decimals, fractions and percentages, using partitioning strategies

or alternatively

• justify the reasonableness of answers to problems solved, using a calculator or algorithm.

• use multiplication and division strategies to solve problems that involve proportions, ratios and rates.