PYP Mathematics Continuum

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1 Counting from One By Imaging to Advanced Counting (-) Y E+ 0- K N O W L E D G E Read,Write, and Count Whole numbers up to 00, forwards and backwards in s, s, 5 s, and 0 s Recall How many tens in a two-digit number, eg 7 has tens Groupings that make up numbers to 0, Y CA+ - Y AC + eg + 7 = 0 Doubles up to 0 and the matching halves, eg =, ½ of is 7 Groupings with 0, eg 0 + = M E N T A L S T R A T E G I E S Solve Addition problems, up to 00, by counting on in my mind Solve and for + = Subtraction problems, up to 00, by counting back in my mind, 7, 6, 5 for 9 = 5 Estimating and measuring area using squares and then showing the area as repeated addition and multiplication facts What kind of shapes have larger or smaller perimeters?

2 Advanced Counting to Early Additive (-5) Y E+ 0- Y CA+ - Y AC + K N O W L E D G E Read and Count Whole numbers up to 000, in ones, tens and hundreds 70, 0, 90, 00, 0 Recall How many tens in a three-digit number, eg 56 has 5 tens All the addition facts to 0, eg + 7 = 5 All the, 0, 5 multiplication facts and the matching division facts, eg 5 5 = 7 Find a unit fraction of: M E N T A L S T R A T E G I E S Using doubles, eg + 7 = 5 because =, 6 = because + = 6 Making tens, eg + 6 = 0 + Joining and separating tens and ones, eg + 5 = (0 + 0) + ( + 5) = 59 Using repeated addition, eg 6 as =, + = Turning multiplications around, eg 0 = 0 A set using halving, eg ¼ of 0 as ½ of 0 = 0, ½ of 0 = 5 A shape using fold symmetry Explore a million by imagining, visualizing, counting and collecting a million using land mark numbers and estimates Estimating and the measuring using simple weight, distance and liquid measuring scales and making scales for graphs Which graphs show the mode, middle number and range most clearly? Bar graphs, pictographs or line graphs? Why? Estimating and measuring the amount different containers can hold using cubes and showing the amounts using repeated and addition and multipication facts Making different D shapes by putting congruent shapes together Talk about how each congruent shape is a fraction of the larger shape Eg: Each triangle is / rd of the trapezium

3 Early Additive to Advanced Additive (5-6) achieved K N O W L E D G E Read and Order Whole numbers up to,000,000 Eg < < 0 9 How many 0 s and 00 s are in whole numbers up to 0,000 Eg 7 tens are in 7 0 Read and order Fractions with the same numerator or denominator Y E+ 0- Y CA+ - Y AC + Eg < 5 and 0 < 0 5 Recall All the basic addition and subtraction facts up to 0, eg 5 = and + 5 = Recall Find a unit fraction of: All the basic multiplication facts up to 0 0 = 00, eg 6 9 = 5 M E N T A L S T R A T E G I E S Using standard place value (00 s, 0 s, s) Eg 7 06 = as 7 00 = 5, 5 6 = 5 Compensating from tidy numbers Eg 79 = as = 55 Reversing the operation Eg 79 = as 79 + = Splitting one factor into parts Eg = ( 0) + ( ) Doubling and halving Eg 5 = 0 = 0 Reversing the operation for division Eg 6 7 = using 9 7 = 6 A set using multiplication Eg 5 of 5 using 5 7 = 5 AND ESTIMATE: Measuring or collecting data and showing it on graphs with different scales of axis Calculate the mean of data shown on bar and line graphs Is it roughly the middle? Compare attributes of D shapes Eg How is the sum of interior angles connected to the number of sides? The use of ratios and scales to enlarge and reduce the size of shapes Equivalent fractions and their relationship to percentages by creating games or models where parts are labelled as fractions, percentages Angles by relating them to turns and fractions of rotations If one quarter of a turn is 90 degrees, half a turn must be Using simple weight, distance and liquid measuring scales and recording the estimates using whole numbers Create patterns using sticks, cubes or shapes, number the patterns, show the rule of the patterns using algebraic equations and all four operations Try to show the rule of a buddies pattern too Number of sticks needed = number of boxes X 5 + Record your patterns using tables, graphs, words and symbols

4 Advanced Additive to Advanced Multiplicative (6-7) K N O W L E D G E Read and Order Decimals to three places Eg 65 < 6 < 60 Equivalent fractions including halves, thirds, quarters, fifths, tenths, hundredths Y E+ 0- Y CA+ - Y AC + Eg 5 = 0 6 and = 75% = 075 How many s, 0 s, 00 s and 000 s are in whole numbers up 0 to Eg 79 is a tenth of 79 Recall All the basic multiplication and division facts up to 0 0 = 00, and 00 0 = 0 Eg 6 9 = 5, 7 = 9 M E N T A L S T R A T E G I E S fractions, decimals, and integers by: whole numbers by: Solve problems with fractions by: Splitting fractions and using equivalent fractions, eg as ( + ) + = ( + ) + = Using standard place value, reversing, and tidy numbers with decimals, eg 7 = as 7 + = or + 00 = 06 Recognising equivalent operations with integers, eg = has the same answer as = + Using standard place value (00 s, 0 s, s), eg 7 56 = as 7 50= 50, 7 6 =, and 50 + = 9, or 6 7 = as 0 7 = 0, 7 =, 0 + = Compensating from tidy numbers, eg 5 9 = as 70 9 = 0 so 5 9 = Splitting factors, eg 5 6 = as 5 = Finding equivalent ratios, eg : is equivalent to : in the same way as 5 = 0 Expressing division answers and remainders as mixed numbers and fractions, eg 5 = 5 = 5 Probability and how it can be expressed on a scale of 0- or as a percentage Creating squares using cubes and expressing the cube using exponential numbers and roots + 5 = Creating cuboids and expressing the cuboids using multiplication and exponential numbers How are they related? Compare the radius, diameter and circumference of circles what do you notice? Make triangles out of squares by folding them diagonally in half Use grid paper What do you notice about the area of triangles compared to squares?

5 Advanced Multiplicative to Advanced Proportional (7-) K N O W L E D G E Find Least common factors and highest common multiples, eg 6 is the HCF of and Read and order Fraction to decimal to percentage conversions for s, s, 5 s, s, 0 s, s, eg 5 = 06 = 60% How many tenths, hundredths, thousandths are in decimals, eg 7 is 70 thousandths Fractions with different denominators, 7 eg 5 < 6 < M E N T A L S T R A T E G I E S Solve problems that involve combining different proportions fractions and decimals by: Solve problems with fractions, ratios and proportions by: Using weighting or averaging, eg 5% of 6 combined with 75% of gives 7 out of 60 (5% of 60) Using standard place value, reversing, and compensating from tidy numbers, eg 07 9 = as 07 =, = 06, and + 06 = 7 Converting from fractions to decimals to percentages, eg 0% of 5 = as 0 5 = 5 = Creating common denominators, eg 5 or = as = = 9 = 0 Using common factors to multiply between and within ratios Eg : as : as : = : (common factor of ) so : = : (multiplying by 7) Partitioning fractions and percentages, eg 5% of 6 = as 0% of 6 = 6, 5% of 6 =, so 6 6 = 06 Y E+ 0- Y CA+ - Y AC + 5