Games for 5th Graders: Decimals, Order of Operations, First Algebra

Fifth grade is the bridge year. Everything before it was arithmetic on whole numbers; everything after it is algebra, and the crossing has three specific planks.

Plank one: decimals as place value, not as a new species. 0.7 is seven tenths — the same column logic as tens and hundreds, continued to the right. Children who learn decimal rules as separate tricks ("line up the dots") get 0.9 > 0.85 wrong, because they compare them as if they were 9 and 85.

Plank two: order of operations. 3 + 4 × 5 is 23, not 35, and this is not arbitrary — multiplication is repeated addition, so it is already grouped. A fifth grader who accepts the rule without that reason will misapply it the first time brackets and exponents appear together.

Plank three: the letter. In x + 7 = 12, x is not a mystery and not a code — it is a number we have not written down yet, and the equation is a balance. Both sides stay equal as long as you do the same thing to each. That single idea carries a student through the next four years.

Also this year: volume of a rectangular prism (which is area with a third dimension), plotting points in all four quadrants, ratio as a comparison rather than a difference, and negative numbers as positions on a line rather than "numbers that are missing".

Tip for the grown-up. Fifth graders will argue about maths if you let them. "Convince me that 0.9 is bigger than 0.85" produces more learning than ten correct exercises.

Continue with ordered pairs, function machine games, adding integers, ratios and proportions and learning games for 4th graders.