This investigation looks into estimating the size of a large population of objects by taking samples and applying some basic mathematics. It encourages sharing of data, refining methods of collection of the data and discussions about the accuracy and limitations of the method used. Jacob’s Method of counting large numbers of objects involves dividing a given area into equal size areas. Estimate (by counting) the population of one square then multiply this by the number of squares in the grid. What happens if you use different size grids ? How do the estimates compare ? What happens if you take all the estimates in the class and find the range and mean ? How close are they all to the real number ? These and many more questions are laid out on the worksheet provided along with a number of prepared pictures with & without grids for printing or viewing on a computer. Content Teachers Notes An overview of Jacob’s Method and a guide to the Worksheets Estimation Worksheet A guide for the students on how to use Jacob’s Method and record the data. A list of questions for discussion. Estimation Crowds Designed to be used as a starter with the student’s worksheet, it contains 2 crowds of different densities. Pupils start with guessing the size of each crowd, then estimate with a 6 square grid & 24 square grid using Jacob’s Method. **Estimation Samples ** 14 pictures to choose from: crowds, stars, trees, bricks, flowers, balloons, birds in flight and more. Pupils estimate with no grid, a 6 square grid & 24 square grid, and are encouraged to experiment further with other grid sizes of their own. Estimation Sample 3 7 more pictures to choose from, but this time the distribution of the populations are not so even or regular, so its more challenging and opens up more questions. They include a football crowd, bubbles, two other crowds, a shoal of fish and a herd of wilderbeast. In all, lots of examples to practice with & food for lively discussion and critical thinking using basic math and could be taken further into investigating bias in crowd counting. Note: All the documents are printable. To view the sample populations with the grids on a computer you will need the Adobe Acrobat Reader on a PC or Mac.

21 Sets of Worksheets on multiplying and dividing by 10, 100 and 1000 provide an abundance of practice material with multiple levels of differentiation allowing you to select the questions that is just right for your pupils. The Worksheets are divided into 2 formats. For the first format, which is really the preparation stage, there is a **place value grid **for each question so pupils can see what is happening to the numbers as they are multiplied or divided. Having grasped this, pupils can then move onto the Worksheets with 20 questions, with one sample place grid displayed to help the pupils if needed. How many Worksheets in each Set ? Almost unlimited because you can randomise the numbers on ALL the Worksheets at the click of a button. Worksheet Set 1 to 3: with Place Value Grid Multiply by 10 Divide by 10 Mix of multiply and divide by 10 Worksheet Set 4 to 6: 20 Questions 4. Multiply by 10 5. Divide by 10 6. Mix of multiply and divide by 10 Worksheet Set 7 to 9: with Place Value Grid 7. Multiply by 100 8. Divide by 100 9. Mix of multiply and divide by 100 Worksheet Set 10 to 12: 20 Questions 10. Multiply by 100 11. Divide by 100 12. Mix of multiply and divide by 100 Worksheet Set 13 to 15: with Place Value Grid 13. Multiply by 1000 14. Divide by 1000 15. Mix of multiply and divide by 1000 Worksheet Set to 18: 20 Questions 16. Multiply by 1000 17. Divide by 1000 18. Mix of multiply and divide by 1000 Worksheet Set 19 to 21: 20 Questions 19. Mix of multiply by 10, 100 or 1000 20. Mix of divide by 10, 100 or 1000 21. Mix of multiply and divide by 10, 100 or 1000 Note These resources work with the official Adobe Acrobat Reader on a Windows or Mac computers.

These resources have been created with a differentiated approach in mind, so for example, pupils can begin by practicing skip counting with 5 up to 100 then at a suitable pace go all the way up to the Challenge Worksheets that mixes questions with skipping 5, 10 & 100 with sequences that start at any number and go all the way to 1000. There are** 17 Sets of Worksheets ** (and 17 Teaching Pages) covering this topic Content Worksheets + Sequence of numbers starts with a … Worksheet 1. Skip Counting by 5s to 100 multiples of 5 Worksheet 2. Skip Counting by 5s to 500. multiples of 5 Worksheet 3. Skip Counting by 5s to 1000 multiples of 5 Worksheet 4. Skip Counting by 5s to 100. random starting point Worksheet 5. Skip Counting by 5s to 500. random starting point Worksheet 6. Skip Counting by 5s to 1000 random starting point Worksheet 7. Skip Counting by 10s to 200. multiples of 10 Worksheet 8. Skip Counting by 10s to 500 multiples of 10 Worksheet 9… Skip Counting by 10s to 1000. multiples of 10 Worksheet 10. Skip Counting by 10s to 200. random starting point Worksheet 11. Skip Counting by 10s to 500. random starting point Worksheet 12. Skip Counting by 10s to 1000. random starting point Worksheet 13. Skip Counting by 100s to 1000 multiples of 10 Worksheet 14. Skip Counting by 100s to 1000 random starting point Challenge 1. Skip Counting by 5s, 10s & 100s to 1000 multiples of 10 Challenge 2. Skip Counting by 5s, 10s & 100s to 1000. random starting point Challenge 3. Skip Counting by 5s, 10s & 100s to 1000 random starting point and skipping randomised How many worksheets are in each set ? Almost unlimited. At the click of a button all numbers are randomised, so the questions change every time which allows you to create new worksheets for extra practice or revision throughout the year or even give groups of pupils in your class different sets of questions. Answers are automatically generated every time a new worksheet is created. The Teaching Pages, designed for the Interactive Whiteboard for whole class learning follow the same pattern as the Worksheets, and like the Worksheets the numbers can be randomised at the click of a button which means there are lots of examples you can play with. To get a more detailed view of these resources and to try out a limited version of the Worksheets / Teaching Page go to PREVIEW: Skip Counting by 5, 10 & 100 to 1000 Note This resource works with the official Adobe Acrobat Reader on Windows or Mac computers.

This set of resources covers addition and subtraction up to 1000 with the visual aid of dienes. There are 8 sets of worksheets for both addition and subtraction, making 16 in total : Addition Worksheet 1 a & b. No exchange or regrouping . Worksheet 2 a & b. Exchange of units (units add up to more than 10) Worksheet 3 a & b. Exchange of 10s( 10s add up to more than 100) Worksheet 4 a & b. Exchange of 10s and units, both 10s and units need regrouping. At each level: Worksheets a: * both numbers to be added are represented by numbers and dienes, so the dienes are essentially a support tool. *- Worksheets b: *pupils have to deduce the two numbers to be added from the dienes blocks and then do the sum. Subtraction Worksheet 1 a & b No exchange, regrouping or borrowing . Worksheet 2 a & b. Exchange 10 into ten units Worksheet 3 a & b Exchange 100 into 10 tens Worksheet 4 a & b. Exchange 10 into ten units and 100 into 10 tens At each level: Worksheets a: the first numbers is represented by a number and dienes, so the dienes are basically a support tool Worksheets b: pupils have to deduce the first number from the dienes blocks and then do the subtraction. The questions on each of the worksheets can be randomised at the click of a button, so the one resource can be used any number of times for classwork, revision, homework, assessments etc. An answer sheet is produced every time. Note These resources work with the official Adobe Acrobat Reader on Windows or Mac computers. To get a more detailed view of these resources and to try out a limited version of one of the Worksheets go to PREVIEW: Addition & Subtraction to 1000 with Dienes

Percentage Bar Graphs provide visual support to help introduce percentages in an informal way by building on the equivalence of 50%, 25% & 75% and their fractions 1/2, 1/4 & 3/4 plus the knowledge that 10% =1/10 and 1/10th of any multiple of 10 or 100 can easily be found by removing the last zero of the number. From this starting point pupils can then proceed to calculate multiples of 5% or 1% of quantities. The Worksheets and Teaching Pages are set at 5 levels 10%, 25%, 50%, & 75% of multiples of 100 10%,20%,30% …90%, of multiples of 10 10%,20%,30% …90% of multiples of 100 5%,10%,15% … 95% of multiples of 10 Any percentage of multiples of 100 Answers will always be whole numbers. The Worksheets are Dynamic and the Teaching Pages Interactive so that at the click of a button the percentages and quantities are randomised providing endless opportunities to practice at each and every level. To get a more detailed view of these resources and to try out a limited version of the Worksheets go to PREVIEW: Introducing Percentages with Visual Support Note These resources work with the official Adobe Acrobat Reader on Windows or Mac computers.

A bundle of resources to learn and practice reading Roman numerals and converting between Roman Numerals and numbers. You have 4 levels to choose from with number ranges 1-20 10-100 100-1000 1000-3999 The Worksheets are dynamic which means that at the click of a button the numbers in the questions are randomised providing an (almost) unending set of questions. Worksheet 1 Convert Numbers to Roman Numerals at the 4 levels listed above. Worksheet 2 Convert Roman Numerals to Numbers at the 4 levels listed above. The Teaching Resources are interactive which means that at the click of a button the numbers in the questions are randomised providing an (almost) unending set of examples. They are designed as a whole class for use with an Interactive Whiteboard or on a computer for one to one tuition. Ideal for introducing this topic and a preparation for the Worksheets. Teaching Page 1 Convert Numbers to Roman Numerals at the 4 levels listed above. Teaching Page 2 Convert Roman Numerals to Numbers at the 4 levels listed above. To get a more detailed view of these resources and to try out a limited version of a Worksheet go to PREVIEW: Roman Numerals Note These resources work with the official Adobe Acrobat Reader on Windows or Mac computers. UK National Curriculum. Year 5 Programme of Study Number. Number and Place value. Read Roman numerals to 1000 (M) and recognise years written in Roman numerals.

This pack of resources covers the Math topics of the Greatest (or Highest) Common Factor (GCF) and the Lowest Common Multiple (LCM). Whilst this may seem a small disconnected topic it is actually packed with a lot of Math that includes practice with multiplication and division, factors, factor pairs, prime numbers and prime factors, the distributive property of multiplication, entering numbers into simple numerical formulae & writing numbers with exponents, all of which are excellent preparation for the algebra work they will be facing later on. As such this resource of 9 Sets of worksheets could be easily spread throughout the year to build up the various competences and complement other topics in your syllabus. The core method used in both is listing and comparing so students get lots of great practice with their multiplication (and division). However additional methods have been included that combine with knowledge of other areas in Math and show the connection between the GCF & LCM. Set 1: Factor Pairs Set 2: Find the Greatest Common Factor of 2 Numbers Set 3: Find the Greatest Common Factor of 3 Numbers Set 4: Prime Factorization Set 5: Find the Greatest Common Factor (GCF) using Prime Factorization Set 6: Change an Addition to Multiplication with the GCF Set 7: Find the Lowest Common Multiple (LCM) of 2 Numbers Set 8 Find the Lowest Common Multiple (LCM) of 2 Numbers using Prime Factorization Set 9: Find the LCM of 2 Numbers using the HCF The worksheets are, as always in Jeff’s Notebooks, (almost unlimited), and differentiated. Why have multiple ranges of numbers for each Set ? This offers the possibility for the student to initially focus on the process and aim of the specific method outlined rather than their skills with multiplication or division. However when ready they can move on to a more challenging set of questions that brings these skills into play. So, how many worksheets are there exactly ? Almost Unlimited. At the click of a button all numbers are randomized, so you can create as many different worksheets as you need for classwork, homework, revision, preparing for assessment, fillers etc and the numbers will change every time. These are straightforward no-prep worksheets that require no extra work. Simply CLICK-PRINT AND GO. This makes them ideal to have printed and ready for a replacement teacher if needed. Teachers Guide This includes notes on the most popular methods used. Answers are automatically generated every time. Note These resources work with the official Adobe Acrobat Reader on Windows or Mac computers.

Compare two fractions with different numerators and different denominators using visual fraction models leading to using a numerical method by finding a common denominator. Reviewing earlier work Whilst the content of these worksheets centres around fractions with different numerators AND denominators they begin with a review of comparing fractions with the same denominator or same numerator with the number line or rectangle bar. There is also a worksheets with purely numerical questions, but you may want to leave this until after beginning the ‘Investigation’. Comparing fractions with 1/2 Again you have the same visual models as above, but you can choose whether the range of values of the denominators are from 3 or 10 or from 8 to 20. Investigating patterns when comparing patterns Here you could decide to investigate an alternative way to compare the fractions above by looking for any simple patterns in the results obtained so far that will allow your students to answer questions on comparing fractions without the need for visual models or a numerical method. Comparing fractions with different numerators and different denominators We now get to the core of the topic. There are 3 levels, all with the choice of using the number line or rectangle bars. Level 1: Denominators are between 3 and 10 Level 2: Denominators are between 3 and 20, but one is a multiple of the other. Here, it may be useful to refer back to the work done on Equivalent fractions as a double check on the answers could be done numerically. Level 3: Denominators are between 3 and 20 Transition from visual models to a numerical method At this point in the process there needs to be a transition from using visual aids to a numerical approach which students will be using in the future. Students get to see that the easiest way to compare two fractions is if they have the same denominators, then there is only the numerators to think about. This is explained firstly through using a visual fraction model which is then linked to the idea of creating a common denominator between the two fractions by multiplying the 2 denominators together (all explained in the Guide). Numerical Worksheets There are 6 basic worksheet templates here: Numerators or Denominators the same Comparing fractions to 1/2 Compare Fractions (1) - Denominators from 3 to 12 Compare Fractions (2) - One Denominator is a multiple of the other Compare Fractions (3) - Denominators from 3 to 20 Compare Fractions (4) - Denominators from 8 to 20 How many worksheets are there in total ? Lots and lots … Answers are automatically generated every time. Note These resources work with the official Adobe Acrobat Reader on Windows or Mac computers.

Divide multi-digit whole numbers by 1 & 2-digit divisor with & without remainders. Do your pupils need practice with a specific one-digit divisor ? Start with dividing 3-Digit by 1-Digit numbers without remainders, and step by step, go as far as you want your students up to dividing 5-Digit by 2-Digit numbers with remainders. This pack has virtually unlimited Worksheets that require no preparation with 5 basic levels of differentiation, multiple other options in between, with or without remainders, with or without visual support. 5 levels of Differentiation ALL with or without remainders ALL with or without graphic support Level 1: 3-digit numbers divided by a 1-digit number. You can select a single divisor from 2 to 9, or have a page of mixed divisors Level 2: 4-digit numbers divided by 1-digit numbers Same choice of divisor as with Level 1. Level 3: 5-digit numbers divided by 1-digit numbers Same choice of divisor as with Level 1 Level 4: 5-digit numbers divided by a multiple of 10, from 10 to 90. You can select a single divisor from 20 to 90, or have a page of mixed divisors Level 5: 5-digit numbers divided by a number from 20 to 99. Separated into 9 unique worksheets - 20-29, 30-39 … to 90-99 With or Without Visual Support Worksheets are presented in two ways: Simply with the divisor dividend and the space ready for the quotient or With the above plus the scaffolding for each step of the process, with arrows indicating the numbers to be drawn down. How can there be virtually unlimited Worksheets ? At the click of a button all the numbers are randomized providing you with a new set of questions for every level, so the same one resource which could be used for classwork, revision, homework, and practice all the year round. FULL Solutions Contains every step of the standard algorithm towards the solution. This for ALL Worksheets. Note These resources work with the official Adobe Acrobat Reader on Windows or Mac computers.

Year 3 programme of study - Number – fractions- recognise and show, using diagrams, equivalent fractions with small denominators. These resources contain three basic approaches to understanding equivalent fractions: Using 2-D shapes in the form of rectangles The number line. The numerical processes with multipliers and divisors. Equivalent Fractions with rectangles Equivalent fractions are modeled using rectangles, each representing the same area of a whole. This is an ideal visual way to introduce equivalent fractions before proceeding onto the using the number line or purely the numerical method. The 4 Sets of Worksheets provide a step by step approach as follows: Worksheet Set 1: Pupils are asked to write down the (equivalent) fractions of two colored-in rectangles. Worksheet Set 2: Pupils colour in the areas on two rectangles that represent two given equivalent fractions. Worksheet Set 3: Given two coloured-in rectangles and the denominators of the equivalent fractions, pupils must determine the numerators and the multiplier that connects the two fractions. Worksheet Set 4: Given two coloured-in rectangles pupils are asked to write down the full fractions coloured-in and the multiplier connecting the two fractions. How many worksheets are in each set ? (almost) Unlimited. At the click of a button the numbers and the corresponding shaded parts of the rectangles are randomised, so you can create as many different worksheets as you need for classwork, homework, revision, preparing for assessment, fillers etc and the numbers will change every time. Equivalent fractions on the number line. Equivalent fractions are located at the same point on the number line. The printable Worksheets consist of question containing 2 number lines divided up into a different number of equal parts between 0 and 1 which the pupils then have to compare Worksheet Set 1: Pupils are asked to write down the equivalent fraction to the one shown taking into account the number of equal parts on the line. Worksheet Set 2: Pupils have to write down the two equivalent fractions indicated on parallel number lines, each number line divided into a different number of equal parts. How many worksheets are in each set ? As with the worksheets with rectangles …almost Unlimited. Answers are automatically generated every time. Note These Worksheets work with the official Adobe Acrobat Reader on Windows or Mac computers.

This collection contains Worksheets and Teaching Pages on multiplying 2-digit, 3-digit, 4-digit and 5-digit numbers by 1-digit numbers using the standard algorithm. It will provide you with all the levels you should ever need to cover this topic for pupils who need a gentle start with 2-digit numbers to the more challenging worksheets with 5-digit numbers. Differentiation is easy and straightforward. At the click of a button you can create a whole worksheet focussed on multiplying a 2,3,4 or 5-digit number by any single digit from 2 to 9 or choose from 5 levels of a mix of multipliers - 2,3,4,5 or 3,4,5,6 or 4,5,6,7 or 5,6,7,8 or 6,7,8,9. Exactly how many worksheets are there? Virtually unlimited. You will have a minimum of 52 worksheets as described above. e.g a page on multiplying 2-digit numbers by 3, or a page dedicated to multiplying 3-digit numbers by 8 etc. BUT click any button all numbers are randomised, creating a brand new worksheet. This means that you can have as many different worksheets for classwork, homework, review, preparing for assessments, or just simply practice at any time to keep the skill alive throughout the whole year. Answers are automatically generated every time. The Teaching Pages when projected onto a screen or interactive whiteboard allows you to go through the standard algorithm for multiplication showing each step of the process to your class. You begin by choosing the multiplier ( 2 to 9) then when you press one of the randomising buttons it changes the multiplicand, so you have an endless set of examples to practice with. As you enter each digit in the answer line you get instant feedback as to whether it is correct or not. Note These resources work with the official Adobe Acrobat Reader on Windows or Mac computers.

This is a large set of differentiated Worksheets providing an (almost) endless source of practicing column addition and subtraction of numbers from 5-Digit to 8-Digit using the formal written method. The first set of worksheets, adding & subtracting a 4-digit number from a 5-digit number, can serve as a useful interim step between adding & subtracting 4-digit numbers and adding & subtracting 5-digit numbers. It helps bridge the gap between these two levels of difficulty and provides a valuable transition in the learning process. The Worksheet Sets are as follows Add a 4- and 5-Digit number & subtract a 4-Digit from a 5-Digit number Add & subtract two 5-Digit numbers Add three 5-Digit numbers Add four 5-Digit numbers Add & subtract two 6-Digit numbers Add three 6-Digit numbers Add four 6-Digit numbers Add & subtract two 7-Digit numbers Add three 7-Digit numbers Add four 7-Digit numbers Add mix (3) of 5-, 6- 7- Digit numbers Add & subtract two 8-Digit numbers Add three 8-Digit numbers Add four 8-Digit numbers Add mix (3) of 6- 7- 8- Digit numbers There are 15 sets of addition and 5 sets of subtraction that build up from smaller to larger numbers and with addition going from adding together 2 numbers up to 4 numbers, it will enable you to set the level of practice that is right for your students to build accuracy, speed and confidence over whatever time frame is necessary. Layout of Questions For all of the above, the questions are presented in 2 layouts: • The standard algorithm, laid out vertically with the questions and answer lines prepared. • The questions are presented in the horizontal format so that your students have to properly align the digits based on their place values, which is essential for accurate addition & subtraction. This practice reinforces the concept of place value and helps students develop a better understanding of how digits in different positions represent different values. ** This format could also be useful for practicing addition with any informal methods that are part of your syllabus or even estimation ** Number Formats For these resources you have a choice of 3 different number formats which will cover most educators’ needs around the world. Your students will come across at least 2 of the formats within their time at school in other curriculum areas • A comma separator - for the USA & UK e.g. 23,334,290 • A space separator - Canada, Australia, many European countries, and the International System of Units (SI) e.g. 23 334 290 • No separator - used in scientific writings, page numbers, years & addresses etc. e.g. 23334290 How many Worksheets in each set? Almost unlimited. At the click of a button all numbers are randomized, and will therefore change every time so you can create as many different worksheets for classwork, homework, revision, preparing for assessment, review before moving on to 5 or more -digits, etc. Answers are automatically generated every time.