Testing conjectures
Term 1 starting in week 5 :: Estimated time: 2 weeks
- Factors, Multiples and Primes (review)
- True or False?
- Always, Sometimes, Never true
- Show that
- Conjectures about number
- Expand a pair of binomials
- Conjectures with algebra
- Explore the 100 grid
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Activities for pupils
Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.
Brackets Expand algebraic expressions containing brackets and simplify the resulting expression in this self marking exercise.
Convoluted Find the runs of four multiples in order as quickly as you can.
Dump-A-Dice Race An online board game for two players involving prime and square numbers and making choices.
Factor Trees Create factor trees to find the prime factors of the given numbers.
Flabbergasted Game This game for one or two players is an exciting challenge to demonstrate an understanding of factors and multiples.
HCF and LCM Calculator A demonstration of how to find the highest common factor (HCF or GCD) and the lowest common multiple (LCM) of two numbers.
Identity, Equation or Formula? Arrange the given statements in groups to show whether they are identities, equations or formulae.
Mix and Math Determine the nature of adding, subtracting and multiplying numbers with specific properties.
Pick The Primes Pick the prime fruit from the tree as quickly as possible. Practise to improve your personal best time.
Prime Numbers Jigsaw Interactive jigsaw puzzles of different types of grids containing prime numbers.
Prime Numbers Video A reminder of what prime numbers and composite numbers are.
Prime Pairs Game A game for two players who take turns to select two numbers that add up to a prime number.
Prime Pips in Pots This is a version of Wari, one of the oldest known games to still be widely played today. It involves small prime numbers.
Prime Square Drag the numbers into the red cells so that the sum of the three numbers in each row and each column is a prime number.
Product Square Arrange the given numbers in a three by three grid to obtain the diagonal, row and column products.
Satisfy Place the nine numbers in the table so they obey the row and column headings about the properties of the numbers.
Scallywags and Scoundrels Arrange the scallywags and scoundrels on the chairs so that the numbers of any two sitting next to each other add up to a prime number.
Sieve of Eratosthenes A self checking, interactive version of the Sieve of Eratosthenes method of finding prime numbers.
Three Prime Sum A self-marking challenge to write each of the given numbers as the sum of three prime numbers.
Three Ways Find three different ways of multiplying four different digits together to get the given target number. There are nine levels for this online challenge.
True or False? Arrange the given statements in groups to show whether they are always true, sometimes true or false.
Venn Diagram Place each of the numbers 1 to 16 on the correct regions on the Venn diagram.
Words and Concepts Fill in the missing words to show an understanding of the vocabulary of equations, inequalities, terms and factors.
Click on a topic below for suggested lesson Starters, resources and activities from Transum.
- Algebra Pupils begin their study of algebra by investigating number patterns. Later they construct and express in symbolic form and use simple formulae involving one or many operations. They use brackets, indices and other constructs to apply algebra to real word problems. This leads to using algebra as an invaluable tool for solving problems, modelling situations and investigating ideas. If this topic were split into four sub topics they might be: Creating and simplifying expressions; Expanding and factorising expressions; Substituting and using formulae; Solving equations and real life problems; This is a powerful topic and has strong links to other branches of mathematics such as number, geometry and statistics. See also "Number Patterns", "Negative Numbers" and "Simultaneous Equations".
- Factors A factor is a whole number that divides exactly into another whole number. We say the first number is a factor of the second number. Prime numbers only have two factors, one and themselves. After becoming familiar with times tables pupils then practise using this knowledge by recognising factors of numbers. There are well known and some less well known divisibility tests that are of some use in solving more complex number problems. Pupils need to know how to find the highest common factor (HCF) of two or more numbers either mentally or using a pen and paper strategy so that they can correctly manipulate fractions and algebraic expressions.
Lesson Starters
Here are some suggestions for whole-class, projectable resources which can be used at the beginnings of each lesson in this block.
1st Lesson
Halloween
Five problems with a Halloween theme.
2nd Lesson
Four Factors
Find four single digit numbers that multiply together to give 120. How many different ways are there of answering this question?
3rd Lesson
Summer Holidays
How many children and how many donkeys are on the beach? You can work it out from the number of heads and the number of feet!
4th Lesson
Pentadd
Five numbers are added together in pairs and the sums shown. What might the five numbers be?
5th Lesson
Four Make 999
Find four numbers from those given that add up to 999. How many different sets of four numbers can be found?
6th Lesson
Half a Pound
If A costs 1p, B costs 2p, etc can you find a word which costs exactly 50p?
Some of the Starters above are to reinforce concepts learnt, others are to introduce new ideas while others are on unrelated topics designed for retrieval practice or and opportunity to develop problem-solving skills.
