Math - Grade 3

GRADE 4

Course Outline 2019-2020 Mathematics

Term 1

 Number and Place Value

  • Read and write numbers up to 10 000.
  • Count on and back in ones, tens, hundreds and thousands from four-digit numbers.
  • Understand what each digit represents in a three- or four-digit number and partition into thousands, hundreds, tens and units.Give a sensible estimate of up to 100 objects, e.g. choosing from 10, 20, 50 or 100.

Number Patterns and Properties 

  • Derive quickly pairs of two-digit numbers with a total of 100
  • Recognize and use factor pairs and commutativity in mental calculations
  • Order numbers to 100; compare 4-digit numbers using the > and < signs.
  • Understand even and odd numbers.
  • Sort numbers, e.g. odd/even, multiples of up to 100.

Number Pairs and Number Families

  • Find and learn by heart all number pairs to 10 and pairs with a total of 20.
  • Partition all numbers to 100 into pairs and record the related addition and subtraction facts.
  • Recognise and begin to know multiples of 2, 3, 4, 5 and 10, up to the tenth multiple. 
  • Round two to three -digit numbers to the nearest multiple of 10 and 100.

Addition and Subtraction

  • Recall and use addition and subtraction facts for 100
  • Practise mental methods with increasingly large numbers to aid fluency
  • Add pairs of three-digit numbers.
  • Add three or four small numbers, finding pairs that equal 10 or 20
  • Mentally subtract a two-digit number from a three-digit number
  • Add and subtract near multiples of 10 or 100 to or from three- digit numbers, 
  • Add any pair of two-digit numbers, choosing an appropriate strategy\
  • Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why
  • Understand that addition can be done in any order, but subtraction cannot. 
  • Add numbers with up to 4 digits using the formal written method of columnar addition where appropriate.

Multiplication and Division

  • Recall multiplication and division facts for multiplication tables up to 12 × 12.
  • Count on in small constant steps such as threes and fours.
  • Know multiplication for 2×, 3×, 4×, 5×, 6×, 9× and 10× tables and derive division facts.
  • Understand multiplication as repeated addition and use the × sign.
  • Recognise and use factor pairs and commutativity in mental calculations count in multiples of 6 and 9.
  • Understand division as grouping and use the ÷ sign.
  • Use place value, known and derived facts to multiply mentally.
  • Solve problems involving multiplying and adding, including using the distributive law to multiply two-digit numbers by one-digit
  • Understand that division can leave some left over.

Geometry

  • Identify, describe, visualise, draw and make a wider range of 2D shapes including a range of quadrilaterals, the heptagon and tetrahedron; use methods to create a range of polygons. 
  • Classify polygons (including a range of quadrilaterals) using criteria such as the number of right angles, whether they are regular or not and their symmetrical properties.
  • Identify lines of symmetry in 2-D shapes presented in different orientations.
  • Complete a simple symmetric figure with respect to a specific line of symmetry.
  • Make patterns by repeatedly reflecting shapes in vertical lines of symmetry.

Fractions and Decimals.

  • Extend understanding of the number system and decimal place value to tenths.
  • Recognise and write decimal equivalents of any number of tenths.
  • Round decimals with one decimal place to the nearest whole number.
  • Compare numbers with the same number of decimal places up to two decimal places.
  • Solve simple measure problems involving decimals to two decimal places.
  • Order and compare two or more fractions with the same denominator (halves, quarters, thirds, fifths, eighths or tenths).
  • Understand that ½ is equivalent to 0.5.
  • Understand the relation between non-unit fractions and multiplication and division of quantities.

Position and coordinates.

  • Describe and identify the position of a square on a grid of squares where rows and columns are numbered and/or lettered
  • Recognise where a shape will be after translations of a given unit to the left/right and up/down on square and triangular grids
  • Use coordinates to describe the position of a point on a grid in the first quadrant
  • Plot specified points on a coordinate grid in the first quadrant
  • Recognise where a shape will be after translations of a given unit to the left/right and up/down on a coordinate grid in the first quadrant

Unit of Measure - Time

  • Read, write and convert time between analogue and digital 12- and 24-hour clocks
  • Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days.

Term 2

Number and Place Value

  • Read and write numbers with one decimal place.
  • Count on and back in 0.1s, 1s, 10s or 100s from any number up to 10,000
  • Read Roman numerals to 100 (I to C) and know that, over time, the numeral system changed to include the concept of zero and place value.
  • Count in multiples of 6, 8, 25 and 1000.
  • Count backwards through zero to include negative numbers.
  • Order a set of random numbers to at least 10,000 including amounts of money and measures involving decimals.
  • Count in fraction steps, e.g. 1/5, 2/5, 3/5

Multiplication & division

  • Recall multiplication facts for 2, 3, 4, 5, 6, 8 and 9x tables and derive associated division facts.
  • Identify patterns of similar calculations, e.g. if I know 7 x 8, I also know
    0.7 x 0.8, 70 x 8, 70 x 80 etc.
  • Multiply and divide numbers by 10, including those which have answers to one decimal place.
  • Double any multiple of 10 or 100. Use estimation and inverse to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

Addition & subtraction

  • Recall addition and subtraction facts for 100.
  • Choose an appropriate strategy to solve a calculation based upon the numbers involved.
  • Estimate and use inverse operations to check answers to a calculation.
  • Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

Fractions

  • Solve problems involving increasingly harder fractions to calculate quantities.
  • Recognise, find and write fractions.

Measurement: length, perimeter and area.

  • Estimate, measure and compare lengths, weights and capacities, choosing and using suitable uniform non-standard and standard units and appropriate measuring instruments.
  • Compare lengths, weights and capacities using the standard units: centimetre, metre, 100 g, kilogram, and litre.
  • Understand that area is a measure of surface within a given boundary.
  • Find the area of rectilinear shapes by counting squares.

Statistics:

  • Interpret discrete and continuous data using appropriate graphical methods, including bar charts and time graphs.
  • Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs.
    Decimals 
  • Add and subtract numbers with up to 4 digits and decimals with one decimal place using the formal   written methods of columnar addition and subtraction where appropriate.

Geometry

  • Describe positions on a 2-D grid as coordinates in the first quadrant.
  • Describe movements between positions as translations of a given unit to the left/right and up/down.
  • Plot specified points and draw sides to complete a given polygon.
  • Complete a simple symmetric figure with respect to a specific line of symmetry.

Term 3

  • Multiplication & division
  • Recall multiplication and division facts for the 12 times table.

Addition and subtraction: Money

  • Estimate, compare and calculate different measures including money in pence, pounds, Dirham and Dollar. 
  • Write amounts of money using decimal notation.
  • Recognise that one hundred 1p coins equal £1 and that each coin is   of £1.

Fraction

  • Understand that a fraction is one whole number divided by another (for example, can be interpreted as 3 ÷ 4).
  • Divide numbers up to 3 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context.
  • Solve problems involving increasingly harder fractions to calculate quantities.

Decimals

  • Identify the value of each digit to two decimal places.
  • Recognise and write decimal equivalents of any number of tenths or hundredths.
  • Recognise and write decimal equivalents to ¼ ; ½ ; ¾ .
  • Find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths.
  • Convert between different units of measure.
  • Round decimals with one decimal place to the nearest whole number.
  • Order and compare numbers with the same number of decimal places up to two decimal places.

Position and direction

  • Describe movements between positions as translations of a given unit to the left/right and up/down

Ongoing concepts

Problem Solving

Using Techniques and Skills in Solving Mathematical Problems

  • Choose appropriate mental strategies to carry out calculations (addition, subtraction, multiplication and division)and explain how they worked out the answer.
  • Explain methods and reasoning orally.
  • Make sense of word problems (single and easy two-step), decide what operations (addition or subtraction, simple multiplication or division) are needed to solve them and, with help, represent them using a concluding statement.
  • Check the answer to an addition by adding the numbers in a different order or by using a different strategy, e.g. 35 + 19 by adding 20 to 35 and subtracting 1, and by adding 30 + 10 and 5 + 9.
  • Check a subtraction by adding the answer to the smaller number in the original subtraction.
  • Describe and continue patterns which count in 2’s up to 1000’s.
  • Make a sensible estimate for the answer to a calculation.
  • Consider whether an answer is reasonable.
  • Reading and calculating time in both analogue and digital time.

Textbooks

  • Rising Star Audio Mental Math
  • Collins Busy Ants Pupil Book 4A
  • Collins Busy Ants Pupil Book 4B
  • Collins Busy Ants Pupil Book 4C

Assessments: Break down of 100% mark

The final grade for the course will be calculated based on:
Multiple forms of formal and informal assessments including CAT 4, GL Assessments, will be used to gain knowledge about a student’s level of understanding. Assessments will be in the form of Mental Math, End of Unit Evaluations, Times Table Quiz, Problem Solving- (group task/written task) and Formal Assessments. All formal test dates will be posted on the communicator.

Next Steps

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