The biggest mistake I see is kids adding the bottom numbers of fractions. We started cutting up paper at Tutorbase and students finally got why you only add the tops. It turns out seeing the pieces makes the math click faster. I usually suggest making fraction strips together so they can watch the sizes change right there on the table. If you have any questions, feel free to reach out to my personal email
Kids usually freeze on fractions because they are scared of getting it wrong, not because the math is actually tough. I see this constantly. If you stop and break the problem into tiny pieces, it helps a lot. Let them explain what is confusing them before you correct anything. Just being patient and noticing the small wins makes the whole thing way less frustrating. If you have any questions, feel free to reach out to my personal email
The most common fractions mistake kids make is adding numerators and denominators separately, like thinking one-third plus one-fourth equals two-sevenths. It happens because they are applying whole number logic to fractions without understanding that the denominator tells you the size of the pieces, not just a number to add. The fastest correction is to go back to something physical. Take two identical pieces of paper and fold one into thirds and the other into fourths. Have the child color one-third on one sheet and one-fourth on the other, then try to combine them. They will immediately see that the pieces are different sizes and cannot just be stacked together, which is the entire reason common denominators exist. Once they understand that fractions only add when the pieces are the same size, finding common denominators stops feeling like an arbitrary rule and starts making intuitive sense. The kids who struggle most with fractions are usually the ones who jumped to procedures before building that hands-on understanding of what fractions actually represent.
The simplest way is to use a real snack or meal as the whole: show a whole pancake or s'more and physically split it into equal parts so each piece is clearly a fraction of that one whole. A common mistake is treating numerators and denominators like separate whole numbers, which you can correct fast by partitioning the same-sized pieces and only adding like parts. Three hands-on activities that work at home or class are measuring pancake mix into partial cups (the squeeze-bottle makes this easy), splitting s'mores or foil-pack dinners into halves and quarters, and using simple card games by lantern light to compare portions. If a child freezes, lower the pressure and give one concrete, doable step—measure one ingredient or make one split—and praise that quick win to rebuild confidence.