Topicm9fcd4806453eb187_1528449000663_0Topic

Multiplication of common fractions and mixed numbers

Levelm9fcd4806453eb187_1528449084556_0Level

Second

Core curriculumm9fcd4806453eb187_1528449076687_0Core curriculum

IV. Common and decimal fractions. The student:

3) reduces and expands common fractions,

 5) presents an improper fraction in the form of a mixed number, and a mixed number in a form of an improper fraction.

V. The operations with common and decimal fractions. The student:

1) adds, subtracts, multiplies, divides common fractions with one or two‑digit denominators and mixed numbers.

Timingm9fcd4806453eb187_1528449068082_0Timing

45 minutes

General objectivem9fcd4806453eb187_1528449523725_0General objective

Matching a mathematical model to a simple situation and using it in various contexts.

Specific objectivesm9fcd4806453eb187_1528449552113_0Specific objectives

1. Multiplying common fractions and mixed numbers.

2. Solving tasks using multiplication of fractions and mixed numbers.

3. Communicating in English; developing mathematical and basic scientific, technical and digital competences; developing learning skills.

Learning outcomesm9fcd4806453eb187_1528450430307_0Learning outcomes

The student:

- multiplies common fractions using reduction;

- calculates a fraction of the number.

Methodsm9fcd4806453eb187_1528449534267_0Methods

1. Brainstorming.

2. Situational analysis.

Forms of workm9fcd4806453eb187_1528449514617_0Forms of work

1. Individual work.

2. Class work.

Lesson stages

Introductionm9fcd4806453eb187_1528450127855_0Introduction

The students revise the method of multiplying common fractions, squares and cubes of fractions and the notion of an irreducible fraction.

When we multiply common fractions we multiply the numerator by the numerator and the denominator by the denominator.

The square of a common fraction is the product of two identical fractions.

The cube of a common fraction is the product of three identical fractions.

The fraction whose numerator is greater or equal than the denominator is called an improper fraction.

Procedurem9fcd4806453eb187_1528446435040_0Procedure

The teacher informs the students they are going to discover the method of multiplying mixed numbers.

The teacher writes the product on the board.

$4\frac{2}{3}·2\frac{3}{5}$

The students discuss how to multiply these numbers.

They use the computers to check their hypothesis.

SLIDESHOW

The conclusion which should be drawn by the students:

To multiply a mixed number it should be converted into an improper fraction first.

Task 1

The students convert a mixed numbers to improper fractions and do the multiplication.

a) $1\frac{1}{20}·1\frac{6}{11}$

b) $2\frac{3}{8}·2\frac{1}{6}$

c) $5\frac{1}{3}·3\frac{1}{5}$

Task 2

The students calculate the squares and the cubes of mixed numbers.

a) ${\left(1\frac{3}{4}\right)}^2$

b) ${\left(1\frac{1}{2}\right)}^3$

c) ${\left(3\frac{1}{3}\right)}^3$

d) ${\left(4\frac{2}{3}\right)}^2$

After completing the task, they come up with the following conclusion:

The square of a mixed number is the product of two identical mixed numbers.

The cube of a mixed number is the product of three identical mixed numbers.

The students do the task using operations on common fractions and mixed numbers.

Task 3

Ann wants to fence her flower‑bed in the shape of an equilateral triangle with the side ofm9fcd4806453eb187_1527752263647_0Ann wants to fence her flower‑bed in the shape of an equilateral triangle with the side of $3\frac{2}{5}$ m. How many metres of the kerb does she have to buy? How much will she pay for the kerb, if the its running metre costs 15PLN?

An extra task:m9fcd4806453eb187_1527752256679_0An extra task:

Peter says: „I thought of a number and multiplied it by $\frac{3}{4}$. Then I multiplied the result by $1\frac{2}{3}$. I added $\frac{1}{6}$ and got $\frac{2}{3}$.” What number did Peter think of?

Lesson summarym9fcd4806453eb187_1528450119332_0Lesson summary

The students do the summarising tasks.

Then they sum up the class drawing the conclusions to memorise:

To multiply the mixed number, it should be converted into an improper fraction first.

The square of a mixed number is the product of two identical mixed numbers.

The cube of a mixed number is the product of three identical mixed numbers.

Selected words and expressions used in the lesson plan

common fractioncommon fractioncommon fraction

mixed numbermixed numbermixed number

natural numbernatural numbernatural number

reducible fractionsreducible fractionsreducible fractions

improper fractionimproper fractionimproper fraction

irreducible fractionirreducible fractionirreducible fraction

multiplication of the fractionmultiplication of the fractionmultiplication of the fraction

multiplication of the mixed numbermultiplication of the mixed numbermultiplication of the mixed number

productproductproduct

simplest formsimplest formsimplest form