Topicm50bee5a1212e3d32_1528449000663_0Topic

Long multiplication of natural numbers by one‑digit numbers

Levelm50bee5a1212e3d32_1528449084556_0Level

Second

Core curriculumm50bee5a1212e3d32_1528449076687_0Core curriculum

II. Calculations on natural numbersnatural numbersnatural numbers. The student:

4) Multiplies and divides natural numbers by one/two/three – digit numbernumbernumber using the long method, mentally in case of simply examples and using the calculator in case of difficult examples.

Timingm50bee5a1212e3d32_1528449068082_0Timing

45 minutes

General objectivem50bee5a1212e3d32_1528449523725_0General objective

Doing simple calculations mentally or using the long method in more difficult examples, using these abilities in practical situations.

Specific objectivesm50bee5a1212e3d32_1528449552113_0Specific objectives

1. Long multiplication of natural numbers by one‑digit numberslong multiplication of natural numbers by one‑digit numbersLong multiplication of natural numbers by one‑digit numbers.

2. Applying multiplicationmultiplicationmultiplication of natural numbersnatural numbersnatural numbers by one‑digit numbersone‑digit numbersone‑digit numbers to do text exercises.

3.Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesm50bee5a1212e3d32_1528450430307_0Learning outcomes

The student:

- does long multiplication of natural numbers by one‑digit numberslong multiplication of natural numbers by one‑digit numberslong multiplication of natural numbers by one‑digit numbers,

- applies multiplicationmultiplicationmultiplication of natural numbersnatural numbersnatural numbers by one‑digit numbersone‑digit numbersone‑digit numbers to do text exercises.

Methodsm50bee5a1212e3d32_1528449534267_0Methods

1. Situational analysis.

2. JIGSAW.

Forms of workm50bee5a1212e3d32_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm50bee5a1212e3d32_1528450127855_0Introduction

Students revise various methods of mental multiplicationmultiplicationmultiplication of natural numbers. They do multiplications using calculators

a) 134 · 2,

b) 532 · 3,

c) 425 · 7.

Discussion – is it easy to do mental calculations with big numbers? Can we do it faster, or is it easier to use the calculator? What devices can we use to multiply two natural numbersnatural numbersnatural numbers? Do we always have such devices with ourselves?

The conclusion of this discussion should be that it is worth to learn multiplicationmultiplicationmultiplication of big numbers without using any special devices.

The teacher informs students that during this class they will learn such method. For starters – multiplying big natural numbersnatural numbersnatural numbers by one‑digit numbersone‑digit numbersone‑digit numbers.

Procedurem50bee5a1212e3d32_1528446435040_0Procedure

Task
Students work individually, using computers. They open the Slideshow and observe how we perform long multiplication of natural numbers by one‑digit numberslong multiplication of natural numbers by one‑digit numberslong multiplication of natural numbers by one‑digit numbers.

[Slideshow]

After having completed the exercise, they present results of their observations.

In order to multiply a multi‑digit number by a one‑digit‑number:
- we write down the multi‑digit number and the one‑digit number below it, so that the one‑digit number is under the ones digit of the multi‑digit number; we put a line under the numbers;
- we multiply the digits of the first element by the one‑digit number, one by one, starting with the ones number;
- we write down the results under the line, in respective rows.m50bee5a1212e3d32_1527752263647_0In order to multiply a multi‑digit number by a one‑digit‑number:
- we write down the multi‑digit number and the one‑digit number below it, so that the one‑digit number is under the ones digit of the multi‑digit number; we put a line under the numbers;
- we multiply the digits of the first element by the one‑digit number, one by one, starting with the ones number;
- we write down the results under the line, in respective rows.

The teacher divides students into 3 persons groups, which work using the JIGSAW method. Each member of the group gets different task from the tasks below. After solving the tasks, students gather in groups that were doing the same task. They discuss the solutions and clarify any doubts. Then, they return to the initial groups and present the solutions to other members.

Task
Calculate, using the long method. Then verify your results using the calculator

a) 231 · 3,

b) 432 · 2,

c) 1432 · 2,

d) 6221 · 4.

Task
Calculate, using the long method. Then verify your results using the calculator

a) 154 · 4,

b) 454 · 2,

c) 2764 · 3.

Task
Calculate, using the long method. Then verify your results using the calculator

a) 254 · 5,

b) 321 · 8,

c) 6143 · 4.

The teacher grades the students’work and clarifies their doubts.

Students work in pairs. After having completed the exercise, they exchange notebooks and verify their solutions using calculators.

Task
Find the numbernumbernumber a that meets the following condition

a) The number a is 5 times greater than 152.

b) The numbernumbernumber a is 6 times greater than 1721.

c) The number a is 3 times greater than 12552.

Task
Do text exercises. Write appropriate long calculations. Give answers

1) Marcin has 36 toy cars and Tomek has 3 times more. How many toy cars does Tomek have?

2) Mum bough 5 towels. Each towel costs 27 zł. How much money did she spend on shopping?

3) The teacher is collecting payments for the school trip. 8 students still haven’t paid. How much money she needs to collect if the trip costs 275 zł?

The teacher grades the students’work and clarifies their doubts.

An extra task:
By what number do we need to multiply 428 so that the product is equal to 2568?m50bee5a1212e3d32_1527752256679_0By what number do we need to multiply 428 so that the product is equal to 2568?

Lesson summarym50bee5a1212e3d32_1528450119332_0Lesson summary

Students do the revision exercises. Then together they sum‑up the classes, by formulating the conclusions to memorise.

In order to multiply a multi‑digit number by a one‑digit‑number:
- we write down the multi‑digit number and the one‑digit number below it, so that the one‑digit number is under the ones digit of the multi‑digit number; we put a line under the numbers;
- we multiply the digits of the first element by the one‑digit number, one by one, starting with the ones number;
- we write down the results under the line, in respective rows.m50bee5a1212e3d32_1527752263647_0In order to multiply a multi‑digit number by a one‑digit‑number:
- we write down the multi‑digit number and the one‑digit number below it, so that the one‑digit number is under the ones digit of the multi‑digit number; we put a line under the numbers;
- we multiply the digits of the first element by the one‑digit number, one by one, starting with the ones number;
- we write down the results under the line, in respective rows.

Selected words and expressions used in the lesson plan

hundreds rowhundreds rowhundreds row

long multiplication of natural numbers by one‑digit numberslong multiplication of natural numbers by one‑digit numberslong multiplication of natural numbers by one‑digit numbers

multiplicationmultiplicationmultiplication

natural numbersnatural numbersnatural numbers

numbernumbernumber

one‑digit numbersone‑digit numbersone‑digit numbers

ones rowones rowones row

tens rowtens rowtens row

thousands rowthousands rowthousands row