Keeping math skills sharp over summer

Why summer is worth a little attention

Math builds on itself more than most subjects. Fractions lean on multiplication facts, equations lean on fractions and negative numbers, and algebra leans on all of it. When a skill gets rusty over ten weeks off, the first unit of the new year can feel harder than it should, and a child who struggles early can decide they are "not a math person" before the year has really started.

Researchers still debate how much students lose over summer, and it varies a lot from child to child. You don't need to settle that question to act sensibly.

The goal isn't to race ahead into next year's book. It's for your child to walk in on the first day with last year's core skills still warm, and with the habit of thinking about numbers intact.

What to review, grade by grade

Focus on the few skills next year's teacher will build on straight away. In California these come from the California Common Core State Standards for Mathematics. If your child is finishing:

• Kindergarten to grade 2: adding and subtracting small numbers until facts within 20 come quickly (the goal by the end of grade 2), place value with tens and ones (and hundreds in grade 2), telling time, and, after grade 2, counting money.
• Grade 3: multiplication and division facts within 100, fractions as numbers on a number line, and finding area by counting or multiplying.
• Grade 4: multi-digit multiplication, equivalent fractions, comparing fractions, and adding fractions with the same denominator.
• Grade 5: adding and subtracting fractions with different denominators, multiplying fractions, decimals to the thousandths, and volume.
• Grade 6: ratios and unit rates, dividing fractions, negative numbers, and writing and evaluating expressions.
• Grade 7: proportional relationships, adding and multiplying with negative numbers, percent problems, and two-step equations.
• Grade 8 and heading into Algebra I or Math I: solving linear equations, slope, the idea of a function, and the rules for exponents.
• Algebra I: function notation, systems of equations, factoring and solving quadratics.

A simple weekly routine

Short and regular beats long and occasional. A routine that fits around camp, travel and lazy mornings is one you will actually keep. Here is one that works for many families:

• Two days a week: ten minutes on one review skill from the list above, then one problem your child explains out loud to you.
• One day a week: math in real life. Let your child double a recipe, compare prices per ounce at the store, or work out how long a drive will take.
• One day a week: a game. Card games like War with multiplication, dice games, dominoes, Sudoku or a board game with money all count.
• Stop while it is still going well. Ending on a success makes the next session easier to start.
• Take a full week off when you travel. A break is fine; it's the whole summer off that tends to hurt.

Everyday math that actually counts

Real situations give your child a reason to care about the answer, and they show that fractions and rates are tools, not just worksheet topics. Cooking is one of the best places to start, because recipes are full of fractions and scaling. Here is a problem a child finishing grade 5 or 6 can work through with you in the kitchen: a pancake recipe uses 3/4 cup of milk to make 8 pancakes, and you want 12 pancakes.

Let your child estimate first. Twelve is more than 8, so the answer should be more than 3/4 cup, but less than double it. An estimate gives them a way to tell whether their final answer makes sense.

How to help without doing it for them

When your child gets stuck, the most useful thing you can do is ask a question rather than show the next step. Questions keep the thinking with your child, which is where the learning happens. If you're rusty on the math yourself, that's fine: these questions work whether or not you know the answer.

• "What is the problem asking you to find?"
• "What do you already know that might help?"
• "Can you guess roughly what the answer should be?"
• "Can you draw it?"
• "How could you check that answer?"

Getting ready in the last two weeks

In the final couple of weeks before school, shift from general practice to a preview. Look at the first unit of next year's course, often listed on the school or district website, and spend a few sessions on the skills it assumes. If your child took the CAASPP math test (given in grades 3 to 8 and 11), the most recent score report shows how they did in a few broad areas of math, which can help you choose what to review.

Keep the tone light. A child who feels confident on day one gets far more out of the first month than one who was drilled all August.