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Comparing using quotients. How many times more? How many times less?

Source: licencja: CC 0.

Porównywanie ilorazowe. Ile razy więcej? Ile razy mniej?

Learning objectives

  • You will learn to compare numbers using quotient to solve text exercises.

Learning effect

  • You compare numbers using quotient to solve text exercises.

Introduction:

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nagranie abstraktu

Think about ways to compare natural numbers? Revise the concepts: a greater numbernumbernumber, a smallersmallersmaller number, a number greater by 3, a numbernumbernumber smallersmallersmaller by 5.

Task 1
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nagranie abstraktu

Insert proper signs in the dotted spaces: <smaller than symbol (<)<>greater than symbol (>)> or =equals sign (=)=

  1. 10 ……… 4,

  2. 96 ……… 12,

  3. 10 ……… 163,

  4. 42 ……… 45.

Task 2
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nagranie abstraktu

Find a numbernumbernumber that meets the following conditions:

  1. is greater than 16 by 4,

  2. is smallersmallersmaller than 25 by 3,

  3. is greater than 48 by 10,

  4. is smallersmallersmaller than 57 by 12.

Task 3
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nagranie abstraktu

Open the slideshow and observe the examples of terms ‘how many times morehow many times morehow many times more?’, ‘how many times lesshow many times lesshow many times less?’ Match proper operations for presented situations.

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Pokaz multimedialny - porównanie. Instrukcja obsługi z poziomu klawiatury: 1. Uruchomienie aplikacji - ENTER, 2. Na każdym ze slajdów czytany jest automatycznie tekst alternatywny po polsku, 3. Przy pierwszym uruchomieniu na pierwszym slajdzie, czytanie tekstu po angielsku - TAB, 4. Przejście między slajdami: do następnego slajdu - TAB, do poprzedniego slajdu - TAB + SHIFT, 5. Przejście do czytania napisu po angielsku - strzałka w górę + strzałka w dół (czyta tekst po angielsku widoczny na slajdzie).
Source: GroMar, licencja: CC BY 3.0.

After having completed the exercise, present your conclusions.

Conclusions:

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nagranie abstraktu
  • If in the exercise there is the phrase ‘how many times morehow many times morehow many times more’, then in the solution we do multiplication.

  • If in the exercise there is the phrase ‘how many times lesshow many times lesshow many times less’, then in the solution we do division.

Task 4
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nagranie abstraktu

Fill in the table:

Number x

8

10

25

30

Number three times greater than number x

Task 5
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nagranie abstraktu

Fill in the table:

Number x

62

34

18

100

Number two times smaller than number x

Task 6
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nagranie abstraktu

Finish the sentences:

  1. numbernumbernumber 5 times greater than 16 is ……...

  2. A number 2 times greater than 48 is ……...

  3. numbernumbernumber 3 times smallersmallersmaller than 60 is ……...

  4. A number 4 times greater than 64 is ……...

Task 7
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nagranie abstraktu

In the picture, there are four towers made of blocks.

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Source: GroMar, licencja: CC BY 3.0.

Fill in the sentences, based on the picture:

  1. The first tower is made of ……… blocks and is ……… times ……… than the third tower, that is made of ……… blocks.

  2. The fourth tower is made of ……… blocks and is ……… times ……… than the third tower, that is made of ……… blocks.

  3. The third tower is made of ……… blocks and is ……… times ……… Than the fourth tower and is ……… times ……… Than the first tower.

Task 8
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nagranie abstraktu

Do the tasks below. Write the calculations and the answer:

  1. One side of the rectangle is 12 cm long and the other is three times shorter. Give the length of the other side of the rectangle.

  2. Tomek has 150 PLN saved and Maciek has two times more. How many savings does Maciek have?

  3. Sir Wojtek has 3 litres of paint. In order to paint the room he needs five times more. How many litres does he need to paint the room?

Task 9

An extra task:

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nagranie abstraktu

Krzyś has 20 cars. Piotruś has two times more cars than Krzyś, but three times less than Franek. How many cars does Franek have?

Do the revision exercises.

Important:

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nagranie abstraktu
  • If in the exercise there is the phrase ‘how many times morehow many times morehow many times more’, then in the solution we do multiplication.

  • If in the exercise there is the phrase ‘how many times lesshow many times lesshow many times less’, then in the solution we do division.

Exercises

Exercise 1
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Wersja alternatywna ćwiczenia: A quarter is 15 minutes and one day is 24 hours. Determine which sentences are true. Możliwe odpowiedzi: 1. One minute is 15 times shorter than one quarter., 2. One hour if 4 times longer than one quarter., 3. One hour is 4 times shorter than one day., 4. One hour is 24 times shorter than one day.
zadanie
Source: GroMar, licencja: CC BY 3.0.
Exercise 2

In the table there are points results of the contest’s participants:

Participant

Kasia

Basia

Tomek

Wojtek

Number of points

12

48

8

24

  1. How many times more points than Tomek did Basia obtain?

  2. How many times more points than Wojtek did Kasia obtain?

  3. How many times less points than Basia did Wojtek obtain?

  4. How many times more points than Wojtek did Tomek obtain?

Exercise 3

Create a text exercise that can be solved using the operation 75 : 5 = 15.

Use the terms you learn during the lesson to write the task.

Exercise 4
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Wersja alternatywna ćwiczenia: Indicate which pairs of expressions or words are translated correctly. Możliwe odpowiedzi: 1. ile razy więcej - how many times more, 2. ile razy mniej - how many times less, 3. porównywanie ilorazowe - comparing using the quotient, 4. znak równości - the equals sign, 5. iloraz - the product, 6. iloczyn - the quotient
zadanie
Source: GroMar, licencja: CC BY 3.0.
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Interaktywna gra, polegająca na łączeniu wyrazów w pary w ciągu jednej minuty. Czas zaczyna upływać wraz z rozpoczęciem gry. Jeden ruch to odkrywanie najpierw jednej potem drugiej karty z wyrazem. Każdy wyraz jest odczytywany. Kolejny ruch to odkrywanie trzeciej i czwartej karty. W ten sposób odsłuchasz wszystkie wyrazy. Nawigacja z poziomu klawiatury za pomocą strzałek, odsłuchiwanie wyrazów enterem lub spacją. Znajdź wszystkie pary wyrazów.
Source: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

Glossary

comparing using the quotient
comparing using the quotient

porównywanie ilorazowe

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wymowa w języku angielskim: comparing using the quotient
equals sign (=)
equals sign (=)

znak równości (=)

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wymowa w języku angielskim: equals sign
greater than symbol (>)
greater than symbol (>)

znak większości (>)

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wymowa w języku angielskim: greater than symbol (>)
how many times less
how many times less

ile razy mniej – jeżeli w zadaniu występuje zwrot „ile razy mniej”, to w rozwiązaniu zadania wykonujemy dzielenie

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wymowa w języku angielskim: how many times less
how many times more
how many times more

ile razy więcej – jeżeli w zadaniu występuje zwrot „ile razy więcej”, to w rozwiązaniu zadania wykonujemy mnożenie

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wymowa w języku angielskim: how many times more
number
number

liczba

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wymowa w języku angielskim: number
product
product

iloczyn

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wymowa w języku angielskim: product
quotient
quotient

iloraz

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wymowa w języku angielskim: quotient
smaller
smaller

mniejsza (liczba)

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wymowa w języku angielskim: smaller
smaller than symbol (<)
smaller than symbol (<)

znak mniejszości (<)

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wymowa w języku angielskim: smaller than symbol (<)

Keywords

comparing using the quotientcomparing using the quotientcomparing using the quotient

greater than symbol (>)greater than symbol (>)greater than symbol (>)

how many times lesshow many times lesshow many times less - if in the exercise there is the phrase ‘how many times less’, then in the solution we do division

how many times morehow many times morehow many times more - if in the exercise there is the phrase ‘how many times more’, then in the solution we do multiplication

smaller than symbol (<)smaller than symbol (<)smaller than symbol (<)