Home>Worksheets>Age 7-11 Reasoning and generalising about numbers or shapes
 Click on the 'change' button and watch the numbers change. Click on the 'print' button to print a pupil worksheet and an answer sheet. The worksheets can be printed providing the password is entered. Buy a password Choose the topic: Primary A: Place value, ordering and rounding B: Properties of numbers & number sequences C: Fractions, decimals & percentages, ratio & proportion D: Mental calculation strategies (+ and -) E: Pencil & paper procedures (+ and -) F: Understanding multiplication & division G: Rapid recall of multiplication & division facts H: Mental calculation strategies (x and divide) I: Pencil & paper procedures (x and divide) J: Using a calculator K: Checking results of calculations L: Solving problems: making decisions M: Reasoning about numbers or shapes N: Problems involving 'real life', money or measures O: Handling data P: Measures Q: Shape and space Secondary A: Applying mathematics and solving problems B: Place value, ordering and rounding C: Integers, powers and roots D: Fractions, decimals, percentages, ratio and proportion E: Number operations and the relationships between them F: Mental methods and rapid recall of number facts G: Calculations: written methods H: Calculations: calculator methods I: Calculations: checking results J: Equations, formulae and identities K: Sequences, functions and graphs L: Geometrical reasoning: lines, angles and shapes M: Transformations N: Coordinates O: Construction & loci P: Measures and mensuration Q: Statistics R: Probability M: 1 3 4 5 6 7 8 9 14 15 16 17 18 19 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 38 39 40 41 42 43 44 46
 History of numbers: Mayan numbers

13 and 17

Find out about the Mayan number system: mental arithmetic problem-solving.
The Mayans wrote their numbers vertically, with each 'digit' being represented by either a set of dots and horizontal lines. They also had a symbol for zero. The value of a dot is 1, a line represents 5. The highest dots and lines represent 20s, ie one dot is 20, two dots is 40 etc.

 M5: Numbers less than 120: recognise Mayan numbers M7: Numbers less than 399: recognise Mayan numbers M8: Mayan times-tables M9: Mayan number sequences 15 + 32 = ? Type 1 addition 28 + ? = 47 Type 2 addition M1:Addition : type 1 M3: Harder addition : type 1 M4a: Addition : type 2 M4b: Harder addition : type 2

M46: Roman numerals

 Six options 1. 1-100 2. 1-500 3. 1000-1499 4. 1500-1899 5. 1900- 6. 1000- current year

 SAT-type questions (age 11)

M14: Circle three numbers that add up to make....

Years 5 and 6 (age 9-11)

Year 6 (age 10-11)

Year 6 (age 10-11)

Years 5 and 6 (age 9-11)

M18: Missing digits: SAT type questions

M19: Missing numbers: SAT type questions: using a calculator

M39: Missing numbers: each missing digit is either one number or another

 Solving problems
Solve puzzles and problems such as

An example of a wall puzzle: five numbers are on the wall. Write the five numbers below the wall on the right bricks in the wall.

Years 5 and 6 (age 9-11)
Wall puzzles

The number on a brick is either the sum, difference or product of the two numbers below.
There are 6 levels of difficulty going from showing 5 numbers on the wall (the easiest) to showing none of the numbers on the wall.
Use the slider to determine how many numbers are on the wall then click on the 'change' button. You will only see the effect when the worksheet is printed

There are three types of worksheet:

Example of Shape Puzzle 1

Year 6
Shape Puzzles

Work out the value of each shape. The total for each row and column is shown.

M22: Shape Puzzle 1: Three of the same shape can appear in a row (see the example on the left, three squares are in the top row.

M23: Shape Puzzle 2: Three of the same shape will not appear in a row.

M24: Shape Puzzle 3: The solutions can be negative numbers.

Years 5-6 (age 9-11)

M25: Sum puzzle New option: choose all triangles, all squares or a mixture.
Write a number in each circle so that the number in each square equals the sum of the two numbers on either side of it. There may be more than one solution for the square arithmagon. The answer sheet will give one set of solutions.

M38: Another sum puzzle
The three numbers in each line must add up to the same total. The total can be shown or hidden, click on the 'total' button.
The number options are: 1. Small whole numbers 2. Multiples of ten 3. Decimals 4 Positive and negative numbers.
Use the other buttons to show a few puzzles or just one.

The options for both worksheets:
1.
Small whole numbers 2. Multiples of 10 3. Decimals 4. Negative numbers

Year 6 (age 10-11)

Complete this multiplication table

M26: Multiplication table 1
M27:
Multiplication table 2 more difficult

Years 5 and 6 (age 9-11)

Complete the magic squares

M28: 3 x 3 magic square
M29:
4 x 4 magic square

Year 5 (age 9-10)

M43: Work out the value of each shape (positive numbers)

Year 6 (age 10-11)

M39: Balancing problems: what is the weight of a gold bar?
Use the 1 ,2 and 3 buttons to generate the problems. Three levels of difficulty:
level 1: small whole number solutions

level 2: multiple of ten solutions

level 3:
gold bars on both sides

M30: Work out what number each shape represents (positive numbers)
M31: Work out what number each shape represents (positive and negative numbers)
M32: Work out the value of each letter (positive numbers)

Years 5-6 (age 9-11)

Functions

M33: What are the missing numbers?: see the example on the left.
The same functions are used in each line. Can be used to develop algebraic thinking, for example, the numbers in the triangles are 4 times the numbers in the squares.

Year 6 (age 10-11)

M36: Function machines: see the example on the left.
Fill in the missing numbers and functions. Click on the '1' button for single functions, '2' for double functions.

Years 5-6 (age 9-11)

M42: Maximum total

 From each grid pick and add four numbers so that each grid total is a maximum. Each chosen number must be from a different row and column. This grid is done for you.

 Find the missing digits

Year 4 (age 8-9)

M34: Find the missing digits (horizontal sums)

M35: Find the missing digits (vertical sums)

Years 5-6 (age 9-11)

M40: Two missing digits The two missing digits are given. Fill them in to make the sums correct.

M41: Missing numbers in a grid The three missing numbers are given. Fill in the missing numbers to make the rows and columns add up to the given totals. Select the number of numbers shown.

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