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Indices Mathematics Stage 4 MA-9NA

Summary of Substrands Duration: 3 weeks

MA3-4NA Start Date:

Completion Date:

Teacher and Class:

Outcomes

Mathematics K-10

› MA41WM communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols

› MA42WM applies appropriate mathematical techniques to solve problems

› MA43WM recognises and explains mathematical relationships using reasoning

MA49NA operates with positive-integer and zero indices of numerical bases

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Overview Key Words Suggested Assessment

Students revise factors and prime numbers investigate divisibility rules and express a number in prime factors. They learn to express numbers in index form to make it easier and apply the index rules with numbers

Index , indices ,base, power , square root, prime factor, divisible, divisibility google, googleplex, exponent.

Express a number in prime factors with indices. Adjusting the number to suit the ability of the student.

Divisibility tests

Rego Content Teaching, learning and assessment Resources

Stage 4 - IndicesStudents:

Investigate index notation and represent whole numbers as products of powers of prime numbers (ACMNA149)

▪ determine and apply tests of divisibility for 2, 3, 4, 5, 6 and 10

verify the various tests of divisibility using a calculator (Problem Solving)

apply tests of divisibility mentally as an aid to calculation (Problem Solving)

▪ express a number as a product of its prime factors, using index notation where appropriate

recognise that if a given number is divisible by a composite number, then it is also divisible by

Revise prime numbers, factors multiplesPre test quick ten questions to know what students know

Use 100 chart for students to find multiples and thus prime numbers

Sieve of Eratosthenes- use youtube clip

Determine the test and apply testsDivide into groups and investigate divisibility and allow students to come up with some tests they will know some already.

Use poem as a starter for tests – students may put it to music or write another poem

Watch power point on divisibility rules

http://www.youtube.com/watch?v=V08g_lkKj6Q sieve of eratosthenes

divisibility

http://www.usu.edu/coreacademy/Materials/2007/Handbooks/FifthGradeA.pdf

http://www.qacps.k12.md.us/comtek/k-5_lessons/Book_5/Divisibility/divisibility_student_resources.htm

http://www.youtube.com/watch?v=0yHYEJz48rA Adam Spencers

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the factors of that number, eg since 660 is divisible by 6, then 660 is also divisible by factors of 6, which are 2 and 3 (Reasoning)

find the highest common factor of large numbers by first expressing the numbers as products of prime factors (Communicating, Problem cSolving)

Express as prime factors

Give students numbers on coloured paper use textas and express numbers as prime factors. Display in the room-Introduce indices to make it more concise

Adjustment easier numbers and more difficult numbers

Divisibility 2, 5, 10

Write a 3 digit number divisible by 3

Show cartoon

Read story scan and put on interactive white board

prime numbers

❑ ▪ describe numbers written in 'index form' using terms such as 'base', 'power', 'index', 'exponent'

▪ use index notation to express powers of numbers (positive indices only), eg 

▪ evaluate numbers expressed as powers of integers, eg 

investigate and generalise the effect of raising a

Use paper folding activity to introduce indices

Have students construct own patterns using the visualising indices

Introduce the words power base index and exponent Make a

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

http://www.scribd.com/doc/53058897/Index-Laws-Folding-Paper-v1 832

Indices song

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negative number to an odd or even power on the sign of the result (Communicating)

▪ apply the order of operations to evaluate expressions involving indices, with and without using a calculator, eg  ,

poster for the wall

Adjustment -easier powers

Investigate and establish a pattern of a negative number to a positive and negative power.

Look at (-1)100 (1)100

and establish the pattern

Remind students with powers are more powerful so must be done first – students need to be careful when entering -32 into calculator

Discuss why it is wrong

http://www.youtube.com/watch?v=wCFSy_JKz3g

❑ Investigate and use square roots of perfect square numbers (ACMNA150)

▪ use the notations for square root and cube root

▪ recognise the link between squares and square roots and between cubes and cube roots,eg  and

▪ determine through numerical examples that: eg  eg 

▪ express a number as a product of its prime factors to determine whether its square root and/or cube root is an integer

Using interactive white board have squares drawn

Start with the side lengths of squares and find the area. Then after doing side lengths of 4 and 5.

Draw a square of 9 and find length of side

Draw a square of 16 and find length of side

Introduce square root symbol

History of square root

Do the same with cube root. Using a cube and side length

Interesting facts and challenging activities for introductions in lessons

http://www.teachmaths-inthinking.co.uk/activities/visualising-indices.htm

Squares and square roots

http://www.mathsisfun.com/square-root.html

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▪ find square roots and cube roots of any non-square whole number using a calculator, after first estimating

determine the two integers between which the square root of a non-square whole number lies (Reasoning)

▪ apply the order of operations to evaluate expressions involving square roots and cube roots, with and without using a calculator,

eg 

explain the difference between pairs of numerical expressions that appear similar, eg 'Is  equivalent to ?' (Communicating, Reasoning)

How do we find a square root without calculator. Show old tables. How do we get this?

Use prime factor tree to find square roots and cube roots

What about 10 Look at the Montessori method

http://www.montessoritraining.net/elementary_program2/courses/mathematics2/sample_lessons.pdf

❑ Use index notation with numbers to establish the index laws with positive-integer indices and the zero index (ACMNA182)

▪ develop index laws with positive-integer indices and numerical bases by expressing each term in expanded

Students discover laws by working with numbers and then noticing a quicker method

Enrichment Mathematics for Secondary Schools by Anne Joshua

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form, eg

 

verify the index laws using a calculator, eg use a

calculator to compare the values of and (Reasoning)

explain the incorrect use of index laws, eg explain why (Communicating, Reasoning)

▪ establish the meaning of the zero index, eg by patterns

verify the zero index law using a calculator (Reasoning)

use index laws to simplify expressions with numerical bases, eg 

Divide students into groups and see if they can find a quicker way to work out the answers

Write questions on the board circulate around the room to see who has correct answer. Stating yes yes no

And then draw attention that some people are doing it quicker

Let them stop and be sworn to secrecy and continue with other

students to see if they can find the answer quickly. Then establish a law

Repeat with other laws.

How do you find the

What 2 integers does

lie between

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Resources for the teaching of Indices

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Cartoon for introduction of indices

Challenge Activity

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ar

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