To begin Good Questions for Math Teaching, K–6,  Peter Sullivan and Pat Lilburn list three features of the good questions they’ve included in the book. These features sing to me.

• Good questions require more than remembering a fact or reproducing a skill.
• It’s possible for students to learn by answering the question.
• There may be several acceptable answers.

Then they provide more than 300 questions organized into 16 topics (money, fractions, decimals, place value, counting and ordering, operations, weight, volume, area, time, length and perimeter, locations and position, two-dimensional shapes, three-dimensional shapes, chance, and data) with questions for each topic organized into Grades K–2, 3–4, and 5–6 (except for decimals where there are questions only for grades 3–4 and 5–6).

I looked at the questions they posed for operations, the cornerstone of the K–6 math curriculum. Here’s a sampling of the 23 questions they included for that topic, with rationales and tips for using each.

1. A basketball player scored 9 points in two games. What could her scores in each of the games be?
This question helps children think about a problem for which there’s a range of possible answers. For young children, decomposing numbers within 10 is an important reasoning strategy. There are ten possible answers, for whether the players scored 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 points in Game 1. Changing the number of points is a way to tailor the question for individual needs.

2. I put some counters into groups with the same number in each group. I can’t remember what I did, but I do remember that I had 12 counters. What might the groups have been?
It’s important to supply children with counters to work on this question. There are four possible answers―two groups of 6, three groups of 4, four groups of 3, and six groups of 2. It’s fine if children don’t report all four possibilities, but for an extra challenge, you might ask a child to find all of the possible answers.

1. Five numbers added together make an odd number. What do you know about the numbers?
This question highlights some features of odd and even numbers. I love a question like this that both provides the opportunity to do a good deal of calculating, with numbers chosen by the child, and also asks children to make a generalization. In order for the sum to be odd, either one, three or five of the numbers must be odd. Would that also be true if the question were to explore six numbers that add to an odd sum?

2. What might the missing numbers be?

Again, this is a question that shows children that problems often have more than one answer. There are a variety of possibilities for choosing the missing numbers in the ones place for the addends, as long as they then determine a sum that has a 2 in the ones place. For a challenge, ask children to find all possibilities, or perhaps three or five possible solutions. If this problem is appealing, you might try a game version I described in a previous blog post: Four Strikes and You’re Out. I’ve found that’s always a favorite.