Mathematics: Tier 3-5: Pat has 5 white beads and 1 black bead in her bag. She asks two friends about the probability of picking a black bead without looking in the bag. Owen says: It is one-fifth because there are five white beads and one black bead. Maria says: It is one-sixth because there are six beads and 1 is black. Which of Pat's friends is correct? Explain why the other friend is wrong.
Tier 4-6: A teacher has 5 bags of marbles and 3 extra marbles. Each bag has n marbles inside. She asks: 'How many marbles are there altogether?' The pupils say: Nia 8n; Vijay 3 + 5n; Sam 8; Jo 15n; Karen 5 x n + 3; Glyn (3+5)n.
a) Name one pupil who is right. b) Name another pupil who is right. c) Choose one right answer. Explain why it shows the right number of marbles. d) There are 88 marbles altogether. Fill in one pupil's right answer to help you complete the equation (space for right answer) equals 88. Solve the equation to find n, the number of marbles in a bag.
Tier 5-7: The same question about beads from tier 3-5, with these additions. Tracy has a different bag of black beads and white beads. The probability of picking a black bead from Tracy's bag is 7 13 . What is the probability of picking a white bead from Tracy's bag?
How many black beads and how many white beads could be in Tracy's bag?
Peter has a different bag of black beads and white beads. Peter has more beads in total than Tracy. The probability of picking a black bead from Peter's bag is also 7 13 . How many black beads and how many white beads could be in Peter's bag?
Tier 6-8: See graphic above
Science: There are two tiers, 3-6, for less advanced pupils, 5-7 for brighter children.
Tier 3-6: The list gives some of the properties of different materials: bends and stretches easily does not bend easily; does not burn burns easily; is hard is soft; is magnetic is not magnetic; sinks in water floats on water.
Complete the sentences with words from the list above: Steel is used for bridges because it (answer) and (answer). Wool is used for clothing because it (answer) and (answer).
Tier 5-7: See graphic below.
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