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Solving word problems

Source: licencja: CC 0.

Rozwiązywanie zadań tekstowych

Learning objectives

  • You will get to know the method of creating a pattern for solving a word problem.

  • You will get to know the method of producing and solving word problems.

Learning effect

  • You will learn to create a pattern for solving a word problem.

  • You will learn to produce and solve word problems.

Recollect the order of operations in multi‑stage arithmetic expressions. Give examples of the most common calculation mistakes. Think and give examples of everyday life situations, in which you use skills connected with addition, subtraction or multiplication. Form short tasks leading to these types of calculations.

This type of tasks is called word problems by mathematicians. The aim of the class will be getting to know methods of solving them. Draw a timeline and mark some important moments in your life on the timeline. Using this information, produce two word problems and solve them. Create a pattern for solving word problems.

The pattern for solving word problems.

  1. Read the problem carefully.

  2. Write down the given information, what is knownknownknown and unknownunknownunknown – you can make a picture or a diagram.

  3. Do the calculations and write them down.

  4. Check if the result meets all the requirements of the problem.

  5. Write down the answeransweranswer.

Task 1
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nagranie abstraktu

Analyse the material in the interactive illustration.

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Ilustracja interaktywna przedstawia tor wyścigowy, na dolnej krawędzi drogi widoczna jest podziałka z liczbami od 1 do 10. Na drodze widać dwa samochody, pierwszy przed linią na wysokości liczby 5, drugi przed linią na wysokości liczby 9. Nad pierwszym samochodem napis: t z indeksem jeden równa się 1 s. Nad drugim samochodem napis: t z indeksem dwa równa się 1 s. Na dole rysunku, po prawej stronie znajduje się znak zapytania obok którego umieszczono numery 1 i 2. Na numerach widoczne są podpisy. 1. At what distance from the starting point will you find both cars after 30 seconds of driving? {audio}, 2. How far will these cars be from each other after 40 seconds of driving? {audio}.
A word problem
Source: GroMar, licencja: CC BY 3.0.

There are many ways of solving word problems. For example, by writing and performing appropriate operation or graphically.

Use the information to solve the tasks.

Task 2
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nagranie abstraktu

Solve the following tasks graphically.

  1. John and Frank set off on a bike trip at the same time, from the same place and they took the same way. John did 5 km during half an hour and Frank did 6 km. What is the distance between John and Frank after 3 hours of the trip?

  2. Ann has got 3 wooden boards. The second board is twice as long as the first one. The length of the third board equals the sum of the lengths of the first and the second board. Calculate the length of the third board, knowing that the first board is 80 cm long.

Task 3
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nagranie abstraktu

Solve the tasks using the pattern for solving word problems.

  1. Susan eats two scoops of icecream every day. How much money does she spend per week if one scoop costs 2,30 zł?

  2. Kinga is 160 cm tall. Jola is 12 cm taller than Kinga. Kasia is 8 cm sorter than Jola. How tall is Kasia?

Having finished all the tasks, do the consolidation tasks. Write down the information you should remember.

The pattern for solving word problems.

  1. Read the problem carefully.

  2. Write down the given information, what is knownknownknown and unknownunknownunknown – you can make a picture or a diagram.

  3. Do the calculations and write them down.

  4. Check if the result meets all the requirements of the problem.

  5. Write down the answeransweranswer.

Exercises

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Exercise 1
Wersja alternatywna ćwiczenia: Decide which sentence is true. Mark’s car needs 9 l of petrol to do 100 km. Możliwe odpowiedzi: 1. The car needs 22,5 l of petrol to do 250 km., 2. The car needs 40 l of petrol to do the distance between Łódź and Krosno (490 km). , 3. The car needs 55 l of petrol to do 550 km.
zadanie
Source: GroMar, licencja: CC BY 3.0.
Exercise 2

Ask two questions about each of these sentences.

  1. There are 6 staircases in a block of flats. There are 16 flats in each of the staircases. There are 7 windows in each of the flats.

  2. Ada had 140 candies. She decided to give them to her classmates. The first four mates got 6 candies each, the other five mates got 5 candies each.

  3. Agnieszka collected colour animal stickers. She had already had 36 when her brother gave her another 11 stickers. It appeared that 8 of them were identical to the ones she had had before. So, she exchanged them for 4 stickers with a friend.

Exercise 3

Solve the task. Describe the metod of solving it in English.

Twins Ewa and Lidka are 24 years old together. Patryk is twice as old as Ewa. How old is he?

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Exercise 4
Wersja alternatywna ćwiczenia: Indicate which pairs of expressions or words are translated correctly. Możliwe odpowiedzi: 1. dana - known, 2. rozwiązanie graficzne - graphic solution, 3. rozwiązanie - solution, 4. odpowiedź - answer, 5. sprawdzenie - method of solving, 6. sposób rozwiązania - checking
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

answer
answer

odpowiedź

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wymowa w języku angielskim: answer
checking
checking

sprawdzenie

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wymowa w języku angielskim: checking
graphic solution
graphic solution

rozwiązanie graficzne

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wymowa w języku angielskim: graphic solution
known
known

dana

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wymowa w języku angielskim: known
solution
solution

rozwiązanie

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wymowa w języku angielskim: solution
metod of solving
metod of solving

sposób rozwiązania

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wymowa w języku angielskim: metod of solving
unknown
unknown

szukane

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wymowa w języku angielskim: unknown
word problem
word problem

zadanie tekstowe

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wymowa w języku angielskim: word problem

Keywords

answeransweranswer

graphic solutiongraphic solutiongraphic solution - rozwiązania, które wymagają stworzenia diagramu

knownknownknown

metod of solvingmetod of solvingmetod of solving

word problemword problemword problem