Y10 Foundation SOW Term 1


Numeracy Focus. • Add, subtract, multiply, divide with negative numbers. • Bidmas. • Estimating answers to calculations. Notes. • Foundation students should constantly be reminded of the 'rules of algebra' and the benefit of using function machines as a means of understanding the order of operations and reverse them to ...

Y10 Foundation SOW Term 1 Algebra Focus  Students should be completely familiar with all the rules of algebra  Plot straight line graphs of functions by setting up a table of x and y points as coordinate pairs (by use of function machines) Numeracy Focus  Add, subtract, multiply, divide with negative numbers  Bidmas  Estimating answers to calculations Notes  Foundation students should constantly be reminded of the ‘rules of algebra’ and the benefit of using function machines as a means of understanding the order of operations and reverse them to solve for unknowns  Confidence and accuracy in working with negative numbers and also using the correct order of operations will be essential for all aspects of the SOW, especially Algebra topics.  Stress the importance and value of being able to estimate answers – estimations allow students to have confidence in their actual answers and instantly recognise whether an answer is likely to be correct or not.  Students should be able to estimate angles too and use this in checking answers. Topic Number: Place value



Learning Objectives Understand place value and order numbers, representing them as positions on a number line (include negative numbers) F

Number: Number operations

 

Add, subtract, multiply and divide with positive and negative numbers E Know the correct order of operations (BIDMAS) D

Grade F

E D

Number: Approximation & calculation

  

Round numbers to a given place value position, decimal place or significant figure D Use approximations to one significant figure to make estimates to calculations C Use calculators effectively & efficiently D/C

D C D/C

Topic Algebra: Arithmetic sequences Algebra: Linear graphs

           

Learning Objectives Generate a sequence from number and diagram patterns D Generate a sequence from a term-to-term rule and a nth term rule C Find and use the nth term of an arithmetic sequence C Identify which terms cannot be in a given sequence C Find outputs for inputs using function machines E Understand inputs & outputs of a function as coordinate pairs D Use axes and coordinates to describe the position of a point in four quadrants D Plot and draw coordinates and graphs of functions of y in terms of x C Understand a linear sequence represents a straight line and can correspond to a function of y in terms of x in the form y = mx +cC Understand the form y = mx + c and the meaning of m and c C Explore the gradients and equations of parallel lines C Recognise equations of horizontal/vertical graphs C

Shape: Angle properties

   

Shape: Angles of polygons

  

Shape: Bearings

 Understand and use bearings E/D Construct scale drawings involving bearings C

Shape: Congruence

 

Estimate and accurately draw angles G Identify acute, obtuse, reflex and right angles E Recall and use properties of angles – at a point, on a straight line, intersecting lines E Understand and use the angle properties of parallel lines – corresponding & alternate angles D/C Give reasons for angle calculations C Know the angle properties of all types of triangles & quadrilaterals D/C Calculate and use the interior/exterior angles of (regular) polygons to solve problems C

Understand congruence and identify congruent shapes D/C

Year 10 Foundation SOW Term 2 Numeracy Focus  Fractions  Using index laws: o Teach alongside index laws in algebra o calculating in standard form Algebra Focus  Expanding and simplifying linear & quadratic expressions o Link to area & perimeter of shapes (without solving) o Link to index laws Investigations and Problem Solving  Pythagoras Proofs – Notes  Confidence and accuracy in working with negative numbers and also using the correct order of operations will be essential for all aspects of the SOW, especially Algebra topics.  Converting between fractions, decimals and percentage will be included in SOW Term 4  Topic Learning Objectives Grade Resources Algebra & number: D  Understand and use power and index notation D Index Laws  Use a calculator to work out powers of a number D C/B Bingo on shared drive  Use index laws to simplify algebraic expressions or number calculations in suitable for start or index form C end  Understand you can only use the index laws with powers of the same base C/B  Include: o

o

Any number or variable to the power of 0 is 1 Any number or variable to the power of 1 is the number or variable itself

Topic Algebra: Expressions

 

Learning Objectives Understand rules of algebra to write & manipulate algebraic expressions Simplify algebraic expressions by collecting like terms



Expand single & double brackets. Include:

o o o

Number: Fractions

Number: Multiples/ Factors

Number: Prime Factors

Shape: Pythagoras

Link to perimeter of shapes 3(x + 2) – 4(2x – 5) Links to area of shapes



Factorise into single brackets

      

Discuss the importance of leaving answers to calculations as fractions as these are ‘exact’ answers Simplify & find equivalent fractions o Ordering fractions Convert between improper and mixed fractions Add & subtract fractions Multiply and divide fractions Calculate a fraction of a quantity Use a calculator to work out fraction calculations

        

Identify factors of a whole number List factors by considering the product of pairs of factors Understand that a prime number only has two factors List multiples by considering the times table of whole numbers Find the HCF and LCM of two numbers Identify factors, multiples and prime numbers Find the prime factor decomposition of positive integers Write a number as the product of its prime factors Find the HCF and LCM of two or three numbers (by use of venn diagram)

   

Round answers accurately to degree required Understand, recall and use Pythagoras Theorem Find the longest missing side, hypotenuse, of a right-angled triangle Rearrange the formula to find the length of a shorter side of a right-angled triangle.

Grade D C C/B C

D C D D/C D/C D/C D E E E E D C C C

C C C

Year 10 Foundation SOW Term 3 Numeracy Focus  Decimals o Accurate rounding skills (required for Pythagoras) o Students lack confidence when calculating with decimals. Suggest removing decimal when calculating, then replace in answer at the end (eg using estimation) o Most objectives can be met through ‘starters’ Algebra Focus  Solving all types of equations o Link to linear equations learnt in term 1 o Use function machines to aid the order and visualise the inverse functions. o Link to area & perimeter of shapes, setting up equations and solving. Investigating and Problem Solving  Investigate which regular polygons tessellate and why. Stencils maybe available to support task. See Lisa. Notes  Confidence and accuracy in working with negative numbers and also using the correct order of operations will be essential for all aspects of the SOW, especially Algebra topics.  Converting between decimals and fractions or percentage will be included in SOW Term 4  Algebra work – much of the skills for solving equations have been learnt previously (term1 - linear equations) – consider this when planning and creating your overview, particularly time needing to be spent on these learning objectives.  Transformations – provide students with prepared grids to save student time Topic Number: Decimals

   

Learning Objectives Estimate calculations involving decimals to ensure decimal point is correctly positioned in the answer Use written methods to calculate with decimals o Ensure students preferred method is accurate & encourage new/improved methods where issues arise Multiply/divide by a number between 0 and 1. Be able to use one calculation to find an answer to another o Eg 322 x 48 = 15456. Using this find 3.22 x 4.8 or 154.6 ÷ 4.8

Grade E E/D

D D

Number: Squares, cubes and roots

  

Recognise and use squares and cubes and corresponding roots Use the square and cube functions on a calculator Understand and use index notation for squares and cubes

E D

Algebra: Solving Linear Equations

 

Understand an equation has an equal sign. A linear equation may be solved by doing the same (inverse) operation to both sides o o

   Algebra: Solving non-linear equations Algebra: Inequalities

C E/D/C

refer to inverse functions and function machines if required Include solutions that may be negative or fractional

Solve linear equations with unknowns on both sides, expanding brackets and simplifying terms, if applicable, first. Be able to create a linear equation from wording or shape and solve to find a solution to the problem Eg perimeter of a shape, angles in a polygon

C/B C/B/A B/A

Solve equations using trial & improvement

C

     

D C B

Be able to list integers that satisfy an inequality Solve linear inequalities by treating them like a linear equation Know that by multiplying or dividing by a negative the inequality sign is reversed. Be able to represent solutions on a number line Solve inequalities that have been combined Eg y ≤ 3y + 2 < 8 + 2y

C B

Topic Shape: Symmetry & Tessellation

Shape: Transformations

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    

Shape: Pythagoras

   

Learning Objectives Recognise reflection symmetry and rotational symmetry of 2D shapes Understand a tessellation is a tiling pattern with no gaps or overlaps Investigate whether regular polygons tessellate

Recognise and visualise lines of symmetry, reflections, rotations and translations Describe and transform 2D shapes using reflections, rotations and translations Understand and use vector notation for translations Describe and transform combinations of transformations Describe and transform 2D shapes using enlargements, including positive and simple fractional scale factors (negative = higher)

Round answers accurately to degree required Understand, recall and use Pythagoras Theorem Find the longest missing side, hypotenuse, of a right-angled triangle Rearrange the formula to find the length of a shorter side of a right-angled triangle.

Grade D

Resources

C C D

See resource folder

D/C

C C

C C C

http://www.ngflcymru.org.uk/vtc/ngfl/mat hs/echalk/enlargement/tea chingTool/enlargementToo l.html

Year 10 Foundation SOW Term 4



Numeracy Focus Ensure students are equally able to use calculator methods for all number work and are not completely dependent on mental methods, particularly for: o o



percentage of quantity proportion – one amount as a proportion of another converting between FDP

Algebra Focus Refer to algebra skills at all times, especially for formulae o

Eg students know that 2a = 2 x a. This also applies to a formula, eg ½ ct = ½ x cost(c) x time (t)

o Investigating and problem solving  Problem solving opportunities within the shape topics & also deriving formulae. I hope to find resources to meet these objectives. Notes  Use some of the learning objectives as starters, especially where they link to other LO’s.  Encourage confidence and accuracy in working with negative numbers and also using the correct order of operations which is essential for all aspects of the SOW, especially substitution into formulae.  Speed (& density) : Avoid use of formula triangles and encourage students to rearrange the formulas in order to change the subject as required. Topic Learning Objectives Grade Resources Number: FDP D  Recognise the equivalence of fractions, decimals and percentages C  Convert between fractions, decimals and percentages by considering its equivalence out of 100 o Remind students to always simplify fractions where possible  Order fractions, decimals and percentages by converting them into equivalences

C



Number: Ratio & Proportion

    

Convert a fraction (where equivalent fraction out of 100 isn’t possible) into a decimal by dividing the numerator by a denominator ((short division – higher GCSE) or calculator method). Include fractions which become recurring decimals. Recognise a recurring decimal and the digits which are repeating Understand & use ratio notation Express ratio in its simplest form, include 3 part ratios Divide a quantity in a given ratio Convert between ratio & proportion (fraction, decimal & %) o o



Understand ratio compares one part relative to one or more other parts where together they make a whole Understand proportion compares one part relative to the whole as a fraction, decimal or %

Solve problems involving ratio & proportion

C

D D/C C D/C

C/B

Number : Percentage



Calculate a percentage of a quantity o

 Calculate new amounts from a percentage increase or decrease Higher Extension  Calculate compound interest & depreciation o

 Number/Algebra/ Shape: Measure conversion Algebra: Formulae Substitution and rearranging

 

Convert between ways of measuring time



o

C E/D C D

D/C B/A

Use bidmas, negative number and calculator skills efficiently when substituting into a formula to calculate the value of an unknown. Understand -42 = -16 but (-4)2 = 16 (particularly on a calculator)

Be able to derive and use a formula given information, using algebraic skills o Eg Perimeter/area of a shape or Salary based on pay & hours worked etc



B A

Understand formulae describe a relationship between two or more variables and are similar to an algebraic equation

Understand numbers can be substituted into formulae just like an equation to work out the value of an unknown. o



Extend to converting between area and volume if possible

Be able to interpret & use cross-curricular formulae o

C C/B

Eg 0.75hrs = 45 minutes or 135 minutes = 2 ¼ hours etc

Convert between metric measures for length o



Be able to compare compound interest to a simple interest problem

Use reverse percentage methods to calculate original amount before a percentage increase/decrease o

E/D/C

Teach non-calculator & calculator method

C

Rearrange a formula to make a different variable the subject o o

Understand the subject of a formula to be the variable on its own before the equals sign. Understand ‘rearrange a formula’ changes the order of the formula to make a different variable the formula.

C/B

o

Use inverse operations in reverse order to rearrange a formula

Y10 Foundation SOW Term 5 Numeracy Focus Algebra Focus o Efficient calculator use required for all parts of this SOW.  Refer to all algebra skills to begin revising for end of year test. o Students should consider bidmas rules when substituting into  shape formulae and functions for plotting graphs. o Continue to encourage estimating for calculations and accurate rounding skills. Problem solving  * Problem solving questions will be available on shared drive. Please use in lessons from time to time to ensure familiarity with this style of question for end of year exams. Notes  Use autograph to demonstrate graphs, transformations of graphs, simultaneous equations etc Topic Learning Objectives Grade Resources Algebra: Graph sketching



Algebra: Real-life graphs Shape: Construction & Loci

  

Shape: Nets, Plans & Elevations

Recognise, draw (using substitution) and sketch the graphs of: linear functions. o Revisit y = mx + c for linear functions

Draw & interpret distance – time graphs Draw & interpret graphs modelling real-life situations Use a ruler and compass o draw standard constructions o Construct a perpendicular line o Construct the perpendicular bisector of a line o Bisect an angle o Construct triangles  Understand that a locus is a path traced around a moving point o Around one point the locus is a circle o Between two points the locus is the perpendicular bisector o The locus of a fixed line is a parallel line o Between two lines the locus is the angle bisector  Solve worded/real-lfe problems using diagrams and loci o o

Analyse 3D shapes through 2D projections and cross-sections Understand a prism has the same cross-sectional area throughout its length

C

D/C B C

C

C D

Use autograph

o o o o o o

Understand a plan of a solid is the view from directly above (bird’s eye view) Understand an elevation is the view from the front or the side of the solid Be able to draw solids on isometric paper Be able to unfold the sides of a solid to create its net to scale Find the surface area of simple 3D shapes using nets to help visualise individual surfaces and their dimensions

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