Remember: To find the biggest, look at each one in turn, remember the biggest so far, and swap it when a bigger one comes. When you run out, the one you remember is the biggest.
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Read the story, then answer.
One tower at a timeAt the robot club's tower contest, six block towers stand in a row in a dark hall. Maya must tell Ms. Park which tower is the tallest, but Bo can peek at just one tower at a time. Bo has a little memory box that can hold one tower. Tower one has four blocks, so the box holds four. Tower two has nine, which is bigger, so Bo swaps it in. Tower three has three, which is smaller, so the box keeps nine. Tower four has twelve, bigger again, so the box holds twelve. Towers five and six have seven and five, so the box keeps twelve. Bo has seen every tower, and the biggest is twelve.
1
Bo keeps the biggest tower so far in his memory box. Tower 1 has 4 blocks, and tower 2 has 9. What does the box hold after tower 2?
4139
2
Tower 3 has only 3 blocks, so the box still holds .
3
Bo swaps the box when the next tower is bigger than the box.
TrueFalse
4
Which tower makes Bo swap the box to twelve?
Tower 3Tower 4Tower 5
5
Which list shows what the box holds after each tower, from tower 1 to tower 6?
Bo puts tower 1 in the box without a swap. After that, for these six towers, he swaps the box times.
10
Mix-up to fix: Maya looks at four towers with 6, 3, 9 and 4 blocks. She picks the last one she saw and says 4 is the biggest. What should she do instead?
Keep the biggest so far in a box: that is 9, so 9 is the biggestPick the first tower, 6Pick the smallest tower, 3
11
Stretch: after three towers the box holds nine, so Bo can stop and say nine is the biggest of all six.
TrueFalse
12
Write six numbers on six cards and turn them over one at a time. After each card, write the number in your hand.
13
Draw Bo's memory box holding the biggest tower after tower 4.
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Answer key · Set A
The tower contest
19 Nine is bigger than four, so Bo swaps it in. The box holds the biggest so far.
29 Three is smaller than nine, so Bo keeps nine in the box.
3True A bigger tower goes into the box in place of the old one. A smaller tower never replaces the biggest so far.
4Tower 4 Tower 4 has twelve blocks, which is bigger than nine.
54, 9, 9, 12, 12, 12 The box only changes when a bigger tower comes, and it never goes back to a smaller one. The last list is just the towers themselves.
6False The last tower is not always the biggest. Here the last tower has only five blocks.
71-A, 2-C, 3-D, 4-B Bigger means swap, smaller means keep, and when the towers run out the box holds the biggest.
84, 1, 3, 2, 5 Look, ask, swap if it is bigger, and repeat. When none are left, the box holds the biggest.
92 The box holds 5, then swaps to 8 at tower 2, keeps 8 for towers 3 and 4, swaps to 11 at tower 5, and keeps 11 for tower 6. That is 2 swaps.
10Keep the biggest so far in a box: that is 9, so 9 is the biggest The last tower is not always the biggest. Keeping the biggest so far, 6 then 9, and keeping 9 for tower 4, gives 9.
11False Stopping early can miss a bigger tower. Every tower must be checked, and tower 4 has twelve.
12Your own words: a grown-up reads it.
Mark each answer, count the right ones and write the score on the sheet.