Mathematics from zero
Numbers: multiple-choice review
Crux Multiple-choice synthesis across the numbers unit: counting, comparing with the greater-than and less-than signs, place value, the role of zero, and the number line.
Your altitude — climbing toward senior
ZeroJuniorMiddleSenior
You are at middle altitude — in the skySix questions that reach across the whole unit. Each one asks you to put two ideas together — counting and the number line, place and value, the comparison signs and which number is bigger — not just to repeat a definition.
Goal
Confirm you can connect counting, comparing, place value, and the number line — the way the four lessons fit into one picture of what a number is.
Quiz
Completed
You count a pile of buttons by touching each one and saying the next number word, ending on 'twelve'. A friend counts the same pile but accidentally touches one button twice. What goes wrong, and why?
Heads-up Counting is matching one word to one object. Counting the same object twice adds an extra count, so the total comes out one too high.
Heads-up Repeating an object does not skip another; it double-counts the repeated one, so the total is too high, not too low.
Heads-up Twelve is a natural number like any other. The only error is the double touch.
Quiz
Completed
Which sign makes a true sentence in the gap: 6 ? 9 ?
Heads-up The sign depends on which number is bigger, not on writing order. 9 is bigger, so the open side must face 9: 6 < 9.
Heads-up Being single digits does not make numbers equal. 6 and 9 sit at different spots on the line, so they are not equal.
Heads-up Only one is true. 9 is the bigger number, so the only correct sign is 6 < 9.
Quiz
Completed
In the number 70, what is the digit 7 actually worth?
Heads-up A digit's worth is the digit times its place. In the tens place a 7 is worth 7 tens = 70, not 7.
Heads-up The 0 does not cancel anything; it is a placeholder that holds the ones place empty so the 7 stays in the tens place.
Heads-up You do not add the digits. Each digit is worth the digit times its place, and the number is the sum of those place values: 70 + 0 = 70.
Quiz
Completed
Why are 305 and 35 different numbers, even though both use the digits 3 and 5?
Heads-up Dropping the 0 slides the 3 from the hundreds place to the tens place, changing 300 into 30. The 0 is a real placeholder, so 305 and 35 are different numbers.
Heads-up More digits matter precisely because of place: the extra place is what makes the 3 worth 300 instead of 30. Place is the reason, not just digit count.
Heads-up They differ in value: 305 is three hundred and five, 35 is thirty-five. The 0 changes what the other digits are worth.
Quiz
Completed
You stand on 4 on the number line and take 3 steps to the right. Where do you land, and what does each step mean?
Heads-up Stepping right is counting up one per step, not multiplying. Three steps right of 4 is 5, 6, 7 — you land on 7.
Heads-up Steps to the right count up, not down. Counting back would be steps to the left. Three steps right of 4 lands on 7.
Heads-up On a real number line every gap is one equal step, so three steps always lands you three numbers along: from 4 to 7.
Quiz
Completed
A drawing labels its marks 0, 1, 2, 3 in order, but the gap from 0 to 1 is tiny and the gap from 2 to 3 is huge. Why is this not a proper number line?
Heads-up Order alone is not enough. Equal gaps are what let the line show distance, not just sequence; uneven gaps make the picture misleading.
Heads-up Starting at 0 is correct — 0 is the anchor every other number is measured from. The real fault is the unequal gaps.
Heads-up Numbers grow to the right, which this drawing gets right. The fault is that the gaps between marks are not equal.
Recap
The through-line of the unit is one picture: counting matches one number word to one object, the number line lays those numbers out in order with equal gaps growing to the right, comparing reads off which number sits further right (and the open side of the sign faces it), and place value explains why the same digit is worth different amounts depending on where it sits — with zero as the placeholder that keeps every digit in its place.