Unit 7 Variations Projects/Maths-Factors_Area... · Web viewRecognise and use multiples, factors (divisors), common factor, highest common factor, lowest common multiple and primes;

Project: Factors, Area and Operations

Project focusNumber work exploring factors and prime numbers. Solving problems involving language of numbers, i.e. factors and multiples. Understanding how factors of numbers relate to area and perimeter problems.Project length 12 lessons

National Curriculum PoS covered include:Links to prior learningYear 6 National Numeracy Plan

Make general statements about odd or even numbers, including the outcome of products.

Recognise multiples up to . Know and apply simple tests of divisibility. Find simple common multiples. Recognise squares of numbers to at least . Recognise prime numbers to at least 20. Factorise numbers to 100 into prime factors. Calculate the perimeter and area of simple compound shapes that can

be split into rectangles.Learning Outcomes. At the end of this project…

New terminology and languageBODMASCompetences developed during this unit

Resources

Links to future learning Recognise and use multiple, factors (divisors), common factor, highest

common factor, lowest common multiple and primes; find the prime factor decomposition of a number.

Use squares, positive and negative square roots, cubes and cube roots, and index notation for small positive integer powers.

Deduce and use formulae for the area of a triangle, parallelogram and trapezium; calculate area of compound shapes made from rectangles and triangles.

Use index notation for integer powers and simple instances of the index laws; know and use the index laws for multiplication and division of positive integer powers; begin to extend understanding of index notation to negative and fractional powers, recognising that the index laws can be applied to these as well.

Know and use the formulae for the circumference and area of a circle, and arcs and sectors of circles.

Suggested Sequence of Activities1. Exploring factors. 2. Exploring primes. 3. Exploring primes. 4. Exploring factors.

5. Lowest Common Multiple.

6. Highest Common Factor.

7. Area: pegboards. 8. Area: pegboards.

9. Area and perimeter.

10. Given answer where’s brackets?

11. BODMAS. 12. Using division.

Key pieces of homework requiredHomework 1 Factors, Area and Operations (Multiples)Homework 2 Factors, Area and Operations (Prime Decomposition)Homework 3 Factors, Area and Operations (Operations)Enrichment(Prime Numbers) PE: Why does David Bechham wear 23? http://www.motivate.maths.org/conferences/conference.php?conf_id=90(Prime Numbers) Music: Music of Primes(Prime Numbers) Biology: Cicadas Predator and Prey (Science Year 8 Summer 3).

Links across the Elmgreen curriculum ICT

© The Elmgreen School 2007 1

http://www.motivate.maths.org/conferences/conference.php?conf_id=90

Strategies for inclusion and misconceptions1. Decomposing a number into a product of its primes, a common error is to

include 1 in the decomposition, or to write the number as the sum of two prime numbers.

Learning Objectives Recognise and use multiples, factors (divisors), common factor, highest common

factor, lowest common multiple and primes; find the prime factor decomposition of a number (e.g. 8000 = 26 × 53).

Know and use the formula for the area of a rectangle; calculate the perimeter and area of shapes made from rectangles.

Know and use the order of operations, including brackets. Know how to use the laws of arithmetic and inverse operations.

Rich Activities1. Factor-pillars are like caterpillars except they have numbers on their

segments and factors on their legs. Here is the factor-pillar for 18:

Use factor-pillars to list the factor pairs and list of factors of a number.

POWERPOINT WORD EXCEL WEB-LINK BOOK REF.

2. This table shows the numbers from 1 to 6 with their factors. The number 4, for example, has factors 1, 2 and 4, with no number in the space for 3. Make your own table for the numbers up to 30. See what you can find out about numbers with only two factors. Can you guess the next one? What sort of numbers are they? Now try three factors and then four factors. See if you can guess the next number with three factors and then with four, and explain why. What sort of numbers has an odd number of factors? Can you find other patterns in your table?


*3. Each group is given cards with numbers from 1 to 100 written on them, there is a space underneath each numbers and this is left blank for students to fill in the divisors of the number.


4. Factor Game: Take it turns to roll the dice and write the numbers in one of the boxes of your grid. Once the boxes are full, you should each have five 2 digit-numbers. Work out all the factors of each of your 2-digit numbers. The winner is the person with the most number of factors.


5. Factors and Multiples Game http://www.nrich.maths.org.uk/public/viewer.php?obj_id=5578&part=index&refpage=monthindex.php

What are the smallest blue numbers that will make a complete chain? What are the largest blue numbers that will make a complete chain?


http://www.nrich.maths.org.uk/public/viewer.php?obj_id=5578&part=index&refpage=monthindex.php


What numbers cannot appear in any chain? What is the biggest difference possible between two adjacent blue numbers? What is the largest and the smallest possible range of a complete chain? (The range is the difference between the largest and smallest values.)


6. The Product Game.POWERPOINT WORD EXCEL WEB-LINK BOOK REF.

7. Dominoes. Fives and threes dominoes: The basic idea is to play dominoes by matching pairs of the same numbers together and adding together the values appearing at either end. Players score points according to whether this total is divisible by either five and/or three. http://www.nrich.maths.org.uk/public/viewer.php?obj_id=1200&part=index&refpage=monthindex.php


8. Start with a number and write down its divisors. Add these divisors together apart from the number itself. For example, the divisors of 12 are 1, 2, 3, 4, 6 and 12. Add these divisors together, apart from the number 12 to give 16. 16 now becomes the second number in the divisor “chain”. The chain continues:

. What numbers go directly to 1? What happens to powers of two, i.e. 2, 4, 8, 16?


9. Artistic Eratosthenes sieveUsing multilink cubes, model the sieve by making a 100 square using different colours for different numbers of factors. What are the numbers with 2 factors? An even number of factors?


10. Exploring Primes:

generates prime numbers for some whole number values of , e.g. . Find the lowest whole number value of which does not generate a prime number.

and is there always a prime number between and ? and are these prime?


11. Use the digits 0, 1, 5, 6, 7 and 8 to make two 3-digit numbers with an HCF of 45.


12. (TOPIC LESSON) Using Excel to calculate LCM and HCF(or GCD), e.g. LCM ( number 1, number 2, …), GCD ( number 1, number 2, …).


13. Product of Prime numbers and Highest Common Factor by using a Venn diagram, c.f. with simplifying fractions.


14. http://www.nrich.maths.org.uk/public/viewer.php?obj_id=5423&part=index&refpage=monthindex.phpExcel investigation Multiples of 3: Take a multiple of three, for example 741.741 are 247 lots of three. The digits in 741 add up to 12. And 12 is a multiple of three. Do all multiples of three have digit sums which are also multiples of three? If they do, why does that happen?


15. Can you make square numbers by adding two prime numbers together?POWERPOINT WORD EXCEL WEB-LINK BOOK REF.

16. Find the ten digit number which uses each of the digits 0 to 9 once and has the following properties:

1. the first digit from the left (the billions digit) is divisible by 1 2. the number formed by the first 2 digits from the left is divisible by 2 3. the number formed by the first 3 digits from the left is divisible by 3 4. the number formed by the first 4 digits from the left is divisible by 4 5. the number formed by the first 5 digits from the left is divisible by 5


http://nrich.maths.org/public/leg.php?group_id=1&code=9&page=1







http://illuminations.nctm.org/LessonDetail.aspx?ID=L272


6. the number formed by the first 6 digits from the left is divisible by 6 7. the number formed by the first 7 digits from the left is divisible by 7 8. the number formed by the first 8 digits from the left is divisible by 8 9. the number formed by the first 9 digits from the left is divisible by 9 10. the number itself is divisible by 10. What is the

number? POWERPOINT WORD EXCEL WEB-LINK BOOK REF.

17. Area:How have "Warmsnug" arrived at the prices shown on these windows?Which window has been given an incorrect price?Explain your reasoning clearly.


18. The numbers 4 and 12 have a special property. and and 16 is a factor of 48. Find some other examples of pairs of number such that their sum is a factor of their product. What conditions must exist for pairs of numbers to be related in this way?


19. Use four multilink cubes. Make as many different shapes as you can. Sketch each of the shapes and write down its surface area. What is the greatest surface area you can make with four cubes? What is the smallest surface are you can make with four cubes. Investigate for different numbers of cubes.


20. Make an eight by eight square, the layout is the same as a chessboard. You can print out and use the square below. What is the area of the square? Divide the square in the way shown by the red dashed lines. Cut along the red lines.Rearrange the four pieces to make a rectangle that has one side of five squares.What is the size of the other side? What is the area of the rectangle you have constructed? Is there a difference between the two areas that you found?Can you explain your results?


21. Disappearing square:


http://nrich.maths.org/public/viewer.php?obj_id=1076


22. Factor Game:

The die is thrown and student put the number rolled in any one of the 9 cells. The aim is to position each number so that is a factor of at least one, and ideally both, of the outside numbers in the same row or column, Students win 0, 1 or 2 points per cell, depending whether the number in that cell is a factor of 0, 1 or 2 of the corresponding outside numbers. Highest score wins.

23.

Students fill in their own 4 by 4 grid with a relevant number in each square, for example, they could have 9, 2, 10, 20 in the top row and so on. Get students in turn to call out a number of their choice. Everyone who has that number crosses it off their grid. Any student who have more than one of the number called, may cross them all off. The first student to cross off all their numbers wins. AssessmentYear 7 Factors, Area and Operations


http://nrich.maths.org/public/viewer.php?obj_id=1075

Documents

Unit 7 Variations Projects/Maths-Factors_Area... · Web viewRecognise and use multiples, factors (divisors), common factor, highest common factor, lowest common multiple and primes;