A Weekly Math Plan for the Summer Break

What a break plan is for

A long break is not the time to race ahead. The aim is that the first week of the new school year feels familiar instead of rusty: the facts are still quick, and last year's topics still make sense. That needs much less time than a school day. A single worksheet page, five days a week, is enough for most students, and a plan that small is one a family can actually keep up for eight or nine weeks.

The shape of a week

• Monday to Thursday: one topic from the year just finished, a different one each day.
• Friday: whichever of that week's four pages went worst, on the same settings. If all four went well, choose one of them on a harder setting.
• Every day: mark the page against the answer sheet the same day, while the student still remembers how they worked each problem.

Keeping the same weekday topics all summer has two advantages. Nobody has to decide what to print each morning, and by August it is easy to see from the marked pages which topic is still causing trouble.

Changing the settings over the summer

The weekday topics stay the same, but the settings change in three stages:

1. The first two weeks: a step easier than where the student finished the school year. A first page that goes well matters more than a first page that is challenging.
2. The middle weeks: the settings the student was working on at the end of the year.
3. The last two weeks: replace one weekday with a gentle preview of next year's first topic on its easiest setting, using the topic's lesson pages before the first worksheet.

Plan 1: after a year of arithmetic

For a student who has spent the year on the four operations with whole numbers. All four topics are in Basic Math.

• Monday, multiplication: both numbers 1 digit, Max Value 9. Every fact from $2 \times 2$ to $9 \times 9$.
• Tuesday, addition: two digits plus two digits, so that carrying can happen in more than one column.
• Wednesday, subtraction: two digits minus one digit, then three digits minus two digits once that is easy.
• Thursday, division: first number 2 digits, second number 1 digit, so that most problems have a remainder.

The first two weeks can use one-digit problems for all four days. In the last two weeks, Thursday can become a first look at fractions, adding with Max Denominator "Up to 6".

Plan 2: after fractions, decimals and percentages

For a student who has finished Basic Math 2 and perhaps started Pre-Algebra.

• Monday, fractions: one operation per week in turn (addition, subtraction, multiplication, division), Max Denominator "Up to 12".
• Tuesday, decimals: one operation per week in turn, 2 decimal places.
• Wednesday, percentages: Find the Part, Find the Percent and Find the Whole in turn.
• Thursday, integers: one operation per week in turn, Number Range "Small (up to ±12)".

Rotating the operation each week means every operation comes round twice in eight weeks without any single page mixing them. In the last two weeks, Thursday can move on to ratios and proportions, where every answer is a whole number.

Plan 3: after a year of algebra

For a student who has finished Algebra and starts Algebra 2 in the autumn.

• Monday, integers: one operation per week in turn, Number Range "Medium (up to ±25)". Sign mistakes are behind many algebra mistakes, so this day is worth keeping.
• Tuesday, simplifying expressions: Medium, then Hard.
• Wednesday, distributive property: Hard, which distributes and then combines the $x$-terms.
• Thursday, solving equations: Medium, then Hard.

In the last two weeks, Wednesday can become polynomial multiplication on Easy. It is the distributive property applied twice, so it follows on directly from the page it replaces.

When a page goes badly

A bad page in the first week is normal; skills come back quickly once they are used again. A topic that is still going badly by the third week is different. For the next week, give that topic two days instead of one and move it a step easier. If the wrong answers keep looking alike, the guide to common algebra mistakes describes how to find the habit behind them, and most of it applies to arithmetic as well.

Shorter breaks

Winter and spring breaks are too short for a full plan. For one or two weeks, the Friday idea on its own works well: a page a day from whichever topic was hardest in the term just finished, or a mixed review of the term's topics, one per day.