Year 8 Key Performance Indicators Maths (Number)

Transcription

1 Key Performance Indicators Maths (Number) M8.1 N1: I can solve problems by adding, subtracting, multiplying and dividing decimals. Use correct notation for recurring decimals, know the denominators of simple fractions that produce recurring decimals, convert a recurring decimal to a fraction. Calculate with decimals. Multiply 2&3 digit numbers and multiply by zero, add and subtract decimals. M8.2 N2: I can problem solve by adding, subtracting, multiplying and dividing negative numbers. Problem solve with negative Complete negative number numbers. calculations using all four operations. M8.3 N3: I can calculate using the order of operations. Solve BIDMAS problems where students put brackets in the correct place. Answer order of operation questions involving all the operations. Understand about indices and roots and that addition and subtraction are equal. Use negative numbers in everyday situations e.g. temperature, money. Use the order of operations to solve problems involving add, subtract, multiply and divide. M8.4 N4: I can write numbers in and out of standard form and use them to answer calculations. Complete calculations with numbers written in standard form. Write and order numbers in standard form. powers of 10. Use the prefixes associated with Add and subtract integers with varying significant figures. Compare and order negative numbers. Answer order of operation questions using addition, subtraction and multiplication. Begin to use standard form and understand what it is used for. M8.5 N5: I can calculate with squares, cubes and roots and understand reciprocals. Simplify surd expressions. Rational and irrational numbers. Reciprocals. Calculate squares, cubes and roots. M8.6 N6: I can express numbers as a product of their primes and use them to find highest common factors and lowest common multiples. Use prime factor decompositions and Venn diagrams to find the lowest common multiple. Express numbers as a product of their primes and find the highest common factor using a Venn diagram. Express numbers as a product of their primes. Can recognise prime numbers.

2 Key Performance Indicators Maths (Shape) M8.7 S1: I can label the parts of a circle and solve problems using the area and circumference of a circle. Use the formulae for length of arcs and area of sectors of circles to solve problems. Solve problems involving circumference and area. Find the area and circumference. M8.8 S2: I can use compound measures to solve speed, distance, time, mass, density and volume problems. Solve problems involving compound Find the mass, density and volume. Calculate speed distance and time. measure. Identify upper and lower bounds. M8.9 S3: I can problem solve by calculating the volume of 3D shapes and use metric and imperial measures. Solve problems using surface area and volume. Solve problems involving capacity. Calculate the surface areas of prisms and cylinders. Know the prefixes associated with 10 to the 9, 10 to the 6, 10 to the 3 (giga, mega and kilo). Calculate the volumes of prisms and cylinders. Convert metric and imperial. M8.10 S4: I can draw the plan, front and side views of a shape. Draw the 3D representation from the Draw the front, side and plan plan, front and side elevations. elevations of a 3D shape. M8.11 S5: I can describe translations and reflections of 2D shapes on a grid. Describe a translation using vector Describe a translation without vector notation. Describe enlargements notation. Describe rotations fully. fully. M8.12 S6: I can solve angle problems. Find the interior and exterior angles Find and give reasons for angles in in a polygon. parallel lines. Represent a 3D shape on isometric paper. Describe a reflection by naming the lines shapes have been reflected in. Identify the scale factor when given the object and the image. Find angles in triangles and quadrilaterals. Label the circle. Find speed, distance and time in simple problems e.g. a car drives 20km in 30 minutes, how fast was it going? Solve problems involving units of measurement (length, capacity and area) convert cm cubed to litres. Recognise when shapes are congruent or similar. Translate, reflect and tessellate objects. Enlarge objects without a centre and rotate shapes around a point. Find angles around a point and on a straight line.

3 M8.13 S7: I can find the area and perimeter of compound shapes. Find the area of shaded regions. Find the area of compound shapes. Find the length of a rectangle given a side and its perimeter. Calculate the area of rectangles, triangles and parallelograms.

4 Key Performance Indicators Maths (Data) M8.14 D1: I can use, compare and calculate probabilities and know that probabilities add to one. Know that if the probability of an event is p, the probability of not occurring is 1-p. Calculate the probability of independent and dependent events. Apply estimated probability to future data. Draw and use tree diagrams to represent outcomes of two independent events. Calculate and compare probabilities. Calculate the probability of two independent events and identify when a game is fair. M8.15 D2: I can draw and interpret different statistical tables, graphs and charts. Construct and use frequency Identify correlation, use a line of best polygons to compare sets of data. fit and construct stem and leaf Draw pie charts. diagrams. M8.16 D3: I can find the averages and the range for grouped data and frequency tables. Identify the class that contains the Calculate the mean and mode from median in a grouped data table. a grouped data table. Design and use a data collection sheet for continuous grouped data. M8.17 D4: I can complete cumulative frequency tables and graphs and use two way tables to solve problems. Find lower and upper quartiles of a set of grouped data using a cumulative frequency chart and box plot. Draw cumulative frequency curves and find an estimate for the median. Problem solve using two way tables. Understand and use the probability scale 0 to 1 and the words that represent probability. List outcomes of two events. Interpret bar graphs and frequency diagrams which are misleading. Discuss factors that could affect data collection. Complete two way tables.

5 Key Performance Indicators Maths (Algebra) M8.18 A1: I can estimate solutions to equations and solve problems using trial and improvement. Solve problems using trial and improvement. Estimate solutions to equations using trial and improvement. Substitute into non linear expressions. M8.19 A2: I can draw linear, quadratic and cubic graphs. Draw cubic graphs. Explain the effect of changing parameters in the quadratic on the graph. Draw a table of values for a quadratic graph with positive and negative values. Solve quadratic equations by reading from the graph. M8.20 A3: I can find the equation of a line going through one or two points. Find the equation of a line through Find the equation of a line. two points. M8.21 A4: I can solve simultaneous equations visually and/or algebraically. Solve simultaneous equations with Solve simultaneous equations different coefficients. algebraically with different Draw and compare graphs using their equations. Find the gradient and y intercept of a linear graph. Find the midpoint, find the intercept. Solve simultaneous equations graphically. coefficients of x or y. M8.22 A5: I can apply the laws of indices to simplify expressions and expand and simplify brackets. Use laws of indices including negative and fractional powers. Evaluate powers of fractions. Simplify algebraic fractions. Expand double brackets with positive and negative coefficients. Use the index laws for multiplication and division so simplify expressions. Expand and simplify two sets of single brackets. M8.23 A6: I can solve different types of equations to find the value of the unknown. Solve equations of involving Solve equations by substituting, brackets and fractions in the form including brackets, powers, fractions (as+/-b)/c=(dx+/-e)/f. and unknown on both sides. Simplify expressions by collecting like terms. Begin to work with indices and explore powers of zero and one. Expand single brackets. Solve two step equations. Substitute into linear expressions. Plot simple linear graphs. Interpret graphs and non linear graphs. Know when lines are parallel or perpendicular. Picture investigation: Find the value of each item Simplify expressions involving the four operations. Calculate small powers and try and link them to the laws of indices. Simplify by collecting like terms. Solve one step equations using the inverse of all four operations.

6 M8.24 A7: I can factorise expressions fully, by taking out the highest common factor Solve quadratic equations with no coefficient of x squared. Factorise a quadratic and factorise a perfect square. Factorise by taking out an algebraic common factor. M8.25 A8: I can solve inequalities and represent them on a number line. Solve inequalities in the form Solve linear inequalities and 13<2x+5<25. represent them on a number line. Represent inequalities on a number line. M8.26 A9: I can generate arithmetic and geometric sequences from their nth terms. Generate any term in a quadratic sequence and find the nth term from a geometric sequence. Generate linear sequences from an nth term and find the nth term of an arithmetic sequence. Substitute integers into simple expressions involving small powers. Recognise the highest common factor of two numbers. Understand the symbols and language associated with inequalities. Substitute into formula expressed in letter symbols.

7 Key Performance Indicators Maths (Ratio) M8.27 R1: I can write ratios, simplify them and divide them into quantities. Solve word problems involving ratio and proportion, recognise the link between ratios and fractions. Divide quantities into a given ratio. Find equivalent ratios and reduce a ratio into its simplest form and write ratios in the form of 1:n M8.28 R2: I can write numbers as fractions and percentages of other numbers. Compare proportions using fractions Express One number as a fraction and percentages. and a percentage of another. M8.29 R3: I can apply the four operations to fractions. Multiply and divide mixed number fractions. Solve worded problems involving adding and subtracting fractions. Divide fractions. Add and subtract mixed number fractions. M8.30 R4: I can compare and order fractions, decimals and percentages. Convert fractions to decimals, order Order fractions by making the fractions by converting them to denominators the same. Compare decimals or equivalent fractions, find and order fractions, decimals and equivalent fdps. Express a quantity percentages. as a simplified fraction or a percentage of another quantity. M8.31 R5: Calculate percentage increase and decrease and work backwards from this. Calculate the original price. Calculate percentage increase and decrease. Calculate any fraction of a quantity. Multiply a fraction by another fraction. Add and subtract fractions with different denominators. Compare two or more fractions with different denominators. Write percentages (and decimals) as fractions. Find percentages involving 1%, 5% and 10% Write objects in ratio form. Find simple fractions e.g. 1/2, 1/3 etc. Multiply a fraction by an integer. Add and subtract fractions with the same denominator. Compare the size of fractions using diagrams. Write decimal as a percentage and vice versa. Can find 10%, 5% and multiples of.