Teacher Guide

Two items both times: the first set runs out of money at the third item, and so does the second. Trying the cheapest first is the quick way to see it.

The choice was not wrong. It was made with the information available, and a sale next week is new information. Students who say the choice was bad are judging a decision by its outcome, which is worth naming.

There is no right number and there is a wrong kind of answer. Anything that compares the saving to what the hour would otherwise have been is good; anything that just says a bigger number is not.

Four weeks at $4, because three weeks is $12 and still short. Rounding down here gets it wrong and looks right. If the price rises $1 a week, the gap only closes by $3 a week, so it takes five weeks.

$50 minus $18 is $32, and counting up from $32 gets there in two jumps: to $40, then to $50.

$6, $2, $7, $3 is $18 and you have $15, so at least $3 has to come out. The $3 is the smallest removal and gets you to exactly $15. Removing the $6 or the $7 also works and leaves change, so there is more than one right answer.

Rounding everything up never underestimates, which is exactly what you want when you are checking whether you have enough. Students who spot that this is the safe direction have understood estimation.

Worth is not a property of the object. It was worth $40 to whoever paid $40 and it is worth $25 to whoever pays $25, and both of those are answers about people rather than about shoes.

Location, speed, what else is sold there, or simply that the people buying it are not comparing. Two plausible reasons is the bar.

The six-box is cheaper each. Which one to buy depends on whether you want ten, and a student who says that has answered better than one who just picks the smaller number.

Five pairs fit and no set of three does, because the three cheapest are $3, $4 and $5, which is $12.

Any plan that adds to $20 or less, with the items listed and the total shown, and one sentence saying what was left out.

Something was spent and not written down. The way to find it is to work backwards from the real amount, and the honest answer is often that you cannot find it and have to start again from today.

Both are defensible and the useful answer names what the money was for. Never going below $3 is only careful if the money had somewhere better to be.

Same total, very different weeks. The one with a single big day is harder to plan around, and a student who says so has read the shape rather than the height.

The week does not change: it is still $10. The picture shrinks: the whole week is two circles, and Thursday's $4 is less than one whole circle. Students who notice that the same money can look big or small depending on the key have found something worth keeping.

Eight weeks gets you $32, which is $2 more than the goal. Students who write 7.5 have done the division and not the question.

$104 minus $30 is $74, and $30 at $2 a week is 15 weeks of saving spent in one go. The second number lands harder than the first.

Both orders finish both goals at week 11. The book first means the book at week 3 and the game at week 11; the game first means the game at week 8 and the book at week 11. The order only decides which one you wait for. Either, with a reason.

An ordering, with no numbers, compared with a partner's. There is no answer key, and nobody's order should be checked against a real home. The disagreement is the discussion.

$180, and the useful half of the answer is what that could have been instead. A subscription nobody canceled is one real-life version of this.

$5 of $20 is one fourth. $5 of $30 is one sixth. The same money is a different fraction, which is week 23 arriving early.

Half of $20 is $10, so a third of $30, a fourth of $40, a sixth of $60. Three answers is the bar and there are many more.

Fractions travel and dollars do not. A student who works that out has found the reason grown-ups talk about percentages.

Six hours against two, for the same object. It is the same thing and it is not the same price, and that is week 28 arriving early.

$48 twice: four hours at $12 and six hours at $8. Same money, two hours of difference, and a student who says which they would rather have, and why, has the point.

$5 an hour, which is worse than any other job on this page. The answer for next time is either a higher job price or an honest estimate of the hours, and saying which is the point.

Five hours of work plus an hour of travel is six. Travel is unpaid and it is still time the thing cost them.

$1 in 10 minutes is a better rate than $3 in 40. The assumption is that the walk is worth nothing in itself, and a student who names that assumption has done better than one who just computes.

Doubling the weekly amount halves the time, and where the extra $5 comes from is the real question. Usually it comes out of the spending in week 24's plan.

The paying back stretches or the unexpected thing does not get paid. There is no third option and finding that out on paper is cheap.

$5 back and $3 saved is $8 a week, which may be more than a student has coming in. If so, the honest answers are to pay back slower or save less, and picking one on purpose is the skill.

Two months, and whether that is faster or slower than week 17's plan depends on their own numbers. Either answer is fine with the arithmetic shown.

Change the behavior or change the plan. Writing the same plan again unchanged is the only wrong answer, and naming which one they chose is the whole exercise.

The page they wish had been in the book is the most useful thing a teacher can send back about this year.

Writing week 1 for somebody younger forces a student to pick numbers that matter to a seven-year-old, which is harder than it sounds and shows whether they understood the idea or the arithmetic.