Dynamic Maths

CfE 3rd Level (Pentagon)

This page contains free Dynamic Worksheets that are roughly aligned with the 3rd level of the numeracy and mathematics Experiences and Outcomes of the Scottish Curriculum for Excellence. If you want resources for other levels of course, go to our Free Resources homepage.

Free Resources:

• Question and Answer Key Facts booklet: Booklet 3 (see other levels of booklet here)

Free Worksheets covering entire course:

• Number revision - mixed questions covering number skills at approximately CfE level 3. Updated January 2013 to allow you to choose which topics to include or exclude.

Free Worksheets covering specific topics at this level:

• Algebra-01: simplifying a linear expression (option to decide how many different letters to allow (up to 3), whether to allow negatives or not, and whether to include constants)
• Algebra-02: simplifying an algebraic expression involving multiplying (options to vary level of difficulty)
• Algebra-04: basic substitution into linear expressions (options to choose magnitude of substitution/coefficients/constants; and to decide whether to allow integers)
• Decimals-02: written add and take away sums
• Decimals-03: multiply and divide by powers of 10 (option to multiply, divide or both; and to vary size of numbers in question)
• Decimals-04: what do you add on to a decimal number to get the next whole number, or the next multiple of 0.1 or 0.01 (option to vary number of decimal places)
• Decimals-05: writing a list of number in order from smallest to biggest (option to vary number of decimal places)
• Decimals-06: completing decimal sequences up and down in tenths, hundredths and thousandths (option to vary number of decimal places and direction (up/down) of count)
• Divide-02: divide by single digit, remainder left at end, pupil has to give remainder as either decimal or fraction (both are given on answer sheet) (option vary whether answer can have at most 1, 3 or infinite decimal places; and how many decimal places answers are displayed to)
• Divide-03: divide within tables - 90 quick questions (option to choose just 2/3/4/5/10 tables, or any table) - remainders can be optionally included
• Divide-04: multiply AND divide by single digit, no remainders (option to vary how many digits are in the answer/question, and to decide whether to allow decimals in question)
• Divide-05: multiply and/or divide by multiples of 10, 100, 1000 or 10000 (no decimals in question or answer) (option to choose maximum power of 10, and to choose between multiplying, dividing or a mixture of both; and to restrict to easier tables)
• Equations-01: simple one-step equations involving adding and taking away
• Equations-02: basic two-step equations or inequations with letters only on left-hand side (option to choose equations, inequations or a mixture - and to vary size of numbers and whether integer solutions are allowed)
• Equations-04: basic one-step equations and inequations involving multiplying (option to vary size of numbers involved; to choose equations, inequations or a mixture; and to allow fractional answers)
• Equations-05: basic one-step equations involving dividing; also an option to allow two-step equations with multiplying as well (option to vary size of numbers involved; to choose equations, inequations or a mixture; and to allow fractional answers [only relevant in equations involving multiplying])
• Fractions-02: work out fractions of a quantity (various options to control size of numbers involved, and overall level of mathematical demand)
• Fractions-03: equivalent fractions - complete the fraction to make them equivalent (option to vary size of denominator)
• Fractions-04: reduce fraction to its simplest form (option to vary size of numbers involved)
• Fractions-05: equivalent fractions, decimals and percentages - complete the table with the equivalences (option to allow percentages to have 1dp or not; and to vary which column is hidden)
• Fractions-06: add and take away fractions and/or mixed numbers (option to vary size of denominator, to allow mixed numbers, and to choose operation)
• Fractions-07: multiply and divide fractions and/or mixed numbers (option to vary size of denominator, to allow mixed numbers, and to choose operation)
• Fractions-08: changing topheavy fractions to a mixed number (option to vary size of numbers involved and various other options)
• Fractions-09: changing mixed numbers to topheavy fractions (option to vary size of numbers involved)
• Fractions-10: mixed add, take away, multiply and divide (option to vary size of denominator)
• Fractions-11: given a list of fractions, identify the ones that are equivalent to a given fraction (option to vary size of denominator, and to decide whether or not to tell learners how many correct answers there are)
• Fractions-12: changing mixed numbers to topheavy fractions AND topheavy fractions to mixed numbers - a mixture of Fractions-08 and Fractions-09 (option to vary size of numbers involved)
• Integers-01: adding and taking away integers (option to choose add, take away, mixed; and to vary size of numbers)
• Integers-02: multiplying and dividing integers within tables (option to choose multiply, divide and mixed)
• Integers-03: mixed: all four operations with two integers (option to vary size of numbers allowed in questions)
• Integers-04: mixed: all four operations with up to three integers (option to vary size of numbers allowed in questions and to decide whether to include questions that require a knowledge of BODMAS)
• Measure-02: convert from one unit to another (option to choose difficulty of multiplication/division involved; and to choose exactly which unit conversions you want to include: choose from m-cm, mm-cm, m-km, m-mm, g-kg, kg-t, ml-l, l-cm³, cm²-mm², m²-cm². Sheets can be made to focus on just one conversion (e.g. grams/kilograms) or to mix them up in whichever combination you choose)
• Measure-03: convert from mixed measurements to decimal measurements (option to choose exactly which unit conversions you want to include: choose from m-cm, mm-cm, m-km, m-mm, g-kg, kg-t, ml-l, l-cm³, cm²-mm², m²-cm². Also option to choose which columns are visible/hidden)
• Measure-04: convert from mixed measurements (e.g. 2m 5cm) to whole number measurements (e.g. 205cm) (option to choose exactly which unit conversions you want to include: choose from m-cm, mm-cm, m-km, m-mm, g-kg, kg-t, ml-l, l-cm³, cm²-mm², m²-cm². Also option to choose which columns are visible/hidden)
• Measure-05: tolerance - identify maximum/minimum values (option to choose exactly which units to include, whether to allow decimal values, and whether to allow tolerances expressed as percentages)
• Measure-06: tolerance - identify which out of a list of values are within the given range (option to choose exactly which units to include, whether to allow decimal values, and whether to allow tolerances expressed as percentages) Note - the mistake with answers not being completely correct should now have been corrected (May 2022). If answers still appear to be coming up wrongly, please contact Dynamic Maths.
• Money-03: complete more complicated wageslips, including potential calculation of overtime, commission, tax, National Insurance and pension as well as gross pay and net pay (option to decide whether to calculate (as opposed to just being given) each of overtime, commission, tax, National Insurance and pension)
• Multiply-01: table squares (option to decide if square is ordered, unordered, whether 1 is included, and whether 11&12 times tables are included)
• Multiply-02: multiply within tables - 90 quick questions (option to allow any table; or to restrict questions to 2/3/4/5/10 tables - also options whether to allow 1 or 0)
• Multiply-04: written multiply sums (options to determine how many digits in each factor, which tables to include, whether to allow one or both factors to be decimals)
• Percentages-03: whole number percentages with a calculator (e.g. 23% of £576) (option to decide whether fractions of one percent (e.g. 2.4%, 17.2%) are allowed)
• Percentages-04: mental percentages (option to decide which percentages are included - many options and to vary level of difficulty of the numbers involved)
• Percentages-05: change test marks to percentages (option to vary denominator; and to choose only percentages that can be easily converted mentally)
• Percentages-07: mental percentages (options to vary difficulty of multiplication/division, and to choose whether to focus on multiples of 10%, multiples of 1% or both)
• Percentages-08: practice mixed percentages annd fractions with a calculator (options to add units)
• Percentages-09: non-calculator percentages - multiples of 1% and optionally 10% (options to decide whether to allow multiples of 10%, whether to allow basic decimal answers and what maximum percentage should be, and level of difficulty of multiplication required)
• Proportion-01: simplify a ratio (option to decide the difficulty of simplification, whether to allow ratios that are already in their simplest form, and whether to allow three-part ratios)
• Proportion-02: given a ratio and one quantity, calculate the values of the other quantity (or quantities) to preserve the ratio (option to decide the scale factor, whether to allow ratios that are already in their simplest form, and whether to allow three-part ratios)
• Proportion-03: proportional circles (where the numbers in each row and column increase in proportion with each other). Find the number in the missing circle (choose the "pentagon" option to have scale factors that may include recurring decimals)
• Rounding-01: rounding to the nearest 10, 100, 1000 etc (option to vary length of original number)
• Rounding-02: rounding decimals to a given number of decimal places (option to vary length of original decimal, and how many significant figures may be required)
• Statistics-03: Mean, median, mode and range (option to vary the size of data sets)
• Statistics-04: Mean from a data set (option to vary size of data sets, magnitudes of numbers involved, and whether or not to allow negative numbers)
• Statistics-05: Median from a data set (option to decide whether or not data is already ordered)
• Statistics-06: There is a data set of between 3 and 8 numbers. One number is hidden. The mean is known. What is the missing number? Designed to be projected onto a SmartBoard rather than printed.
• Time-01: Time intervals (options to choose levels of mathematical complexity)
• Time-03: Speed-Distance-Time table (options to choose whether to find speed, distance, time or a mixture)
• Time-04: Converting units of time from mixed units into whole numbers or vice versa (e.g. change 208 minutes into hours and minutes, or change 3 hours 28 minutes into minutes) (options to choose which direction to convert in, and which units are included [hours/minutes, minutes/seconds, days/hours, years/months, weeks/days])
• Time-05: Time as a decimal (e.g. change 2·08 hours into hours and minutes, or change 2 hours 5 minutes into hours) (options to choose which direction to convert in, how many decimal places, and which units are included [hours/minutes, minutes/seconds, days/hours, years/months, weeks/days])
• WholeNumbers-01: count up and/or down in 1, 10, 100, 1000 etc (option to vary increase and/or decrease)
• WholeNumbers-03: writing numbers in millions and billions in full and ordering (2½million, 3.7 million, ¾ billion etc) - NO ANSWERS
• WholeNumbers-04: generate a random number from 1 to 12 digits to display via a projector for pupil(s) to read out loud (option to vary number of digits)
• WholeNumbers-06: add and take away sums (written method (stacking sums/chimney sums)) (option to vary number of digits; and whether add/take away or a mixture)
• WholeNumbers-07: write numbers (given in word) in figures from hundreds up to trillions (option to vary length of number, and whether to include numbers such as "2½ million", "5¾ billion", "2.4 million" etc)