Exempeluppgifter i årskurs 3, 2010, 2011 och 2012

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Exempel på uppgifter från 2010–2013 års

ämnesprov i matematik för årskurs 3

Engelsk version

Äp3Ma13 Part B 2

Äp3Ma13 Part B 3

Innehåll Inledning ................................................................................ Fel! Bokmärket är inte definierat.Written methods ................................................................................................................................ 6Mental arithmetic, multiplication and division .............................................................................. 8Mental arithmetic, addition and subtraction .................................................................................. 8Odd numbers and positioning system ............................................................................................ 9Similarities, number line and number sequences ........................................................................ 12Division of numbers ........................................................................................................................ 14Area, numbers as fractions and estimating of length ................................................................. 16Time ................................................................................................................................................... 18Geometrical objects ......................................................................................................................... 20Patterns .............................................................................................................................................. 23Problem solving ................................................................................................................................ 25The four operations ......................................................................................................................... 28Statistics ............................................................................................................................................. 30

Äp3Ma13 Part B 4

Äp3Ma13 Part B 5

Inledning Detta material innehåller exempel på uppgifter, som inte längre omfattas av sekretess, från ämnesprovet i årskurs 3, 2010–2013. Ett syfte med materialet kan vara att elever i årskurs 3 får bekanta sig med hur uppgifter till ett nationellt prov kan se ut. Ett annat kan vara att föräldrar får en inblick i nationella prov för årskurs 3. Syftet med samtliga nationella prov är i huvudsak att • stödja en likvärdig och rättvis bedömning och betygssättning • ge underlag för en analys av i vilken utsträckning kunskapskraven uppfylls på skolnivå,

på huvudmannanivå och på nationell nivå. De nationella proven kan också bidra till • att konkretisera kurs- och ämnesplanerna • en ökad måluppfyllelse för eleverna. I de lägre årskurserna kan proven även utgöra ett underlag för läraren att stödja eleverna i att utvecklas vidare kunskapsmässigt. Ett viktigt inslag för att allsidigt och kvalitativt bedöma elevernas visade kunskaper och kunskapsutveckling i matematik är att analysera hur eleverna arbetar med och behärskar matematik i olika uppgifter och situationer. • Har eleven försökt lösa uppgiften? • På vilket sätt har eleven arbetat med uppgiften? • Vad har eleven förstått och vilka begrepp har eleven kunskaper om och kan använda? • I vilken utsträckning har eleven klarat de numeriska beräkningarna? • I vilken utsträckning har eleven analyserat, värderat och dragit slutsatser av resultat? Det är väsentligt att eleverna ges möjlighet att visa sina kunskaper på olika sätt och det måste finnas en möjlighet att studera hur eleven resonerar både skriftligt och muntligt. Det är viktigt att eleven får möjlighet att reflektera över sin och andras strategier, förklara och argumentera för sina egna lösningsmetoder och lyssna på andras.

Äp3Ma13 Part B 6

Written methods Write down the method you used to work this out and write your answer. 1. 128 + 63 = Answer:______________ 2. 27 + 98 = Answer:______________

Äp3Ma13 Part B 7

Write down the method you used to work this out and write your answer. 3. 100 – 63 = Answer:______________ 4. 83 – 39 = Answer:______________

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Mental arithmetic, multiplication and division 5. a) 3 ´ 3 = ____ b) 2 ´ 8 = ____

6. b)

122= ____

c)

155= ____

Mental arithmetic, addition and subtraction 7. a) 5 + 9 = ____ b) ____ = 6 + 8 8. a) 15 – 12 = ____ b) ____ = 16 – 7

Äp3Ma13 Part B 9

Odd numbers and positioning system 9. Four of the numbers are odd. Circle them.

10. Here are three cards. Nova made this number using these cards.

Write a number that is smaller and another number that is greater

than Nova’s number. Use the same cards as Nova used.

3 7 0

smaller

Nova’s number

greater

552

85 74

17

39

421 66

30

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11. Write the number that is a) three units less than 35 __________ b) two hundreds less than 765 __________ c) one ten less than 462 __________ 12. Write the number that is a) four hundreds greater than 513 __________ b) two units greater than 14 __________ c) six tens greater than 36 __________

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13. In Egypt they wrote numbers using other symbols. Here is what the numbers 324, 212 and 403 could look like.

324 212 403

a) How much is one of each symbol worth?

= ______________

= ______________

= ______________

Write the numbers 451 and 510 using Egyptian symbols.

451 510

b) c)

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Similarities, number line and number sequences 14. Write the missing numbers in the spaces. a) ____ + 3 = 17 b) 7 + 3 = ____ + 4 c) 14 = ____ + 6 d) 18 = 3 ´ ____ 15. Write the missing numbers in the spaces. a) ____ – 6 = 10 b) 8 – 3 = 9 – ____ c) 16 – ____ = 7 16. Mark each number with an X on the number line.

Write the number under each X. a) 30 b) 65 c) 83

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17. What number should be where the cross is? Write the number.

18. What number should be where the cross is?

Write the number.

19. The numbers are arranged in a sequence.

Continue the sequence. a) 5 10 ____ 20 ____ ____ b) 140 130 120 ____ ____ ____ c) 2 5 8 11 ____ ____ ____

0 1000 500 ´

0 1000 500 ´

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Division of numbers 20. Nova’s mother has 678 Crowns. a) What bills and coins might she have

and how many of each? b) Give another suggestion.

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Write the numbers in order of size. 21. Start with the smallest number. a) 41 70 17 74 14 ______ ______ ______ ______ ______ b) 324 423 234 431 334 ______ ______ ______ ______ ______ 22. Now start with the biggest number. 876 679 807 709 768 ______ ______ ______ ______ ______

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Area, numbers as fractions and estimating of length 23. Nova and Troj want to make a rug to put on the floor in their tree house.

They have 3 pieces of rug to use. They try different ways of placing these pieces.

Nova’s way Troj’s way

a) Which statement agrees with the figures? Mark with an X. Nova’s rug covers the largest surface on the floor,

that is it has the largest area. c Troj’s rug covers the largest surface on the floor,

that is it has the largest area. c Both rugs cover the same surface on the floor,

that is they have the same area. c b) Explain how you know this.

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24. This is Nova and Troj’s flag.

a) What fraction of the flag is blue? b) What fraction of the flag is red? 25. Troj is 120 cm tall.

About how high is the flagpole? Show your solution and write the answer.

Answer: _________________________

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Time 26. What is the time when Nova and Troj start school?

Answer:________________________ 27. The time is

What is the time half an hour later? Answer:________________________ 28. Troj starts eating lunch When he has finished

at 11.00 o’clock. the time is

For how many minutes did he eat lunch?

Answer:______________________

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29. Nova went to sleep She woke up at 21.00 o’clock. at 07.00 o’clock.

For how many hours did she sleep?

Answer:______________________ 30. Write the unit that fits in.

Seconds (sec), minutes (min) or hours (h). a) It takes about 20 _________ to eat lunch at school.

b) It takes about 2 _________ to brush your teeth.

c) It takes about 2 _________ to watch a film on TV.

d) It takes about 1 _________ to say the word Hello!

e) It takes about 10 _________ to sleep at night.

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Geometrical objects 31. Write the geometric name of the object in the box.

a)

b)

c)

d)

e)

f)

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32. Describe a circle.

✎ 33. Describe a square.

✎ 34. What are the differences between these figures?

✎

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35. What geometric name does the object have?

a)

________________________

b)

________________________

c)

________________________

d)

________________________

sphere cuboid cube pyramid

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Patterns 36.

a)

b)

37.

Draw how the pattern continues.

The figures get bigger and bigger. Draw the fourth and fifth figures.

1 2 3

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38. Nova sees an image in her telescope. She has started to draw this image. Complete the drawing so that the pattern will be symmetrical

39. Troj has started drawing another image.

Complete this picture that Troy has started so that the pattern will be symmetrical.

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Problem solving 40. Three films cost 150 kronor altogether.

How much does each film cost, if all films cost the same amount? Show your solution and write the answer.

Answer: _________________________ 41. Troj buys three space pencils.

He pays with a 100 kr bill. He gets back 10 kr in change. How much does each pencil cost? Show your solution and write the answer.

Answer: _________________________

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42. Troj and Nova have 24 kr each. Make three other suggestions as to what balls and how many of each

you might buy for exactly 24 kr.

Suggestion 1 Suggestion 2 Suggestion 3

I will buy twelve Mars balls for my 24 kr.

Planet bouncing Saturn ............. 12 : - Jupiter ............... 6: - Earth................... 3: - Mars .................... 2: -

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43. Space creatures have either one eye or three eyes. Fifteen eyes are staring at Nova and Troj. How many space creatures might that be? Give three different suggestions.

Suggestion 1 Suggestion 2 Suggestion 3

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The four operations 44. Draw a line connecting each picture with the expression

that corresponds to it.

45. a) Circle the expression that gives the greatest answer.

Try to do this without calculations. 42 + 42 3 ´ 42 b) Circle the expression that gives the greatest answer.

Try to do this without calculations.

1002

1004

2 ´ 3 + 2

3 ´ 2 + 1

4 ´ 2 + 1

One picture is left over.

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46. Write a story problem that suits 17−5 =12 47. Write a story problem that suits 3 ´ 6 = 18

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Statistics

Look at the picture showing cuddly animals! 48. a) How many of each kind are there?

Complete the table.

Cuddly animals Number

Lamb

Dolphin

Rat

Parrot

Ladybird

b) Make a bar chart using the table.

1

2

3

4

6 5

7

Number

Cuddly animals Lamb Dolphin Rat Parrot Ladybird

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