This series of 5 word problems lead up to the final problem. Most students should be able to answer the first two questions without too much difficulty. The decimal numbers may cause some students trouble, but if they make a drawing of the road that the girls are riding on, and their positions at the different times, it may help. The third question has a bit of a challenge in that students won't land on the exact meeting time by making a table with distance values every hour. The fourth question addresses a useful concept for problems involving objects moving at different speeds which may be new to sixth grade students.

While students need to be able to write sentences describing ratio relationships, they also need to see and use the appropriate symbolic notation for ratios. If this is used as a teaching problem, the teacher could ask for the sentences as shown, and then segue into teaching the notation. It is a good idea to ask students to write it both ways (as shown in the solution) at some point as well.

The first of these word problems is a multiplication problem involving equal-sized groups. The next two reflect the two related division problems, namely, "How many groups?" and "How many in each group?"

The purpose of this task is to show three problems that are set in the same kind of context, but the first is a straightforward multiplication problem while the other two are the corresponding "How many groups?" and "How many in each group?" division problems.

In this set of addition and subtraction word problems students are encouraged to find their own way to solve the problems. This enables students to discover the strengths and weaknesses of different solution methods and to see how multiple methods all arrive at the same answer. Included with the problem set are tips for getting started, the solutions, a teacher resource page, and a printable student page.

The purpose of this task is to help students articulate their addition strategies and would be most appropriately used once students have a solid understanding of coin values.

Building on their fifth grade experiences with operations on decimal numbers, sixth grade students should find the task to be relatively easy. The emphasis here is on whether students are actually fluent with the computations, so teachers could use this as a formative assessment task if they monitor how students solve the problem.

In this problem students practice addition and subtraction (and possibly multiplication) while developing systematic work strategies. Given two types of ladybirds, each with either 4 or 7 spots, learners explore ways of combining them to achieve different total numbers of spots. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, and links to related games.

This word problems helps students learn to build the biggest three-digit number given any three numbers between 0 and 9 to use as digits.

This collection of division word problems prompts learners to use a variety of methods of division. Allowing learners to choose their own method to solve the word problems enables them to see the strengths and weaknesses of various methods and to see why certain methods might be better for specific problems. Included with these problems is the solution, teacher resource page, tips on getting started, and a printable student page.

This activity gives students a chance to make estimates and comparisons of the measures of length (height) and capacity. It presents an image of a tiny elf next to a normal size mug. Students are asked to estimate the Little Man's height and compare it with that of other objects. Next, they are asked to estimate the height and volume of the Little Man's mug. The Teachers' Notes page includes suggestions for implementation, discussion questions, and ideas for extension and support.

In this instructional task students are given two inequalities, one as a formula and one in words, and a set of possible solutions. They have to decide which of the given numbers actually solve the inequalities.

This problem allows students to explore introductory multiplication and division concepts in the context of sharing cookies ("biscuits" in the UK). Cookies are displayed in two different arrays, and students are challenged to divide them equally among two, three, five, and six people and to deal with remainders. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, and a printable sheet (pdf).

In this problem students apply different strategies to solve a problem involving multiples and remainders. The problem provides clues about dividing a specific number of lollipops equally and asks solvers to determine possible totals. The problem presents three partial approaches and asks solvers to complete them. This resource includes hints for getting started, previously submitted solutions, and a teacher page with implementation suggestions, discussion questions, and differentiation strategies.

The purpose of this task is for students to compare two options for a prize where the value of one is given $2 at a time, giving them an opportunity to "work with equal groups of objects to gain foundations for multiplication." This context also provides students with an introduction to the concept of delayed gratification, or resisting an immediate reward and waiting for a later reward, while working with money.

This problem uses the context of a growing plant in which to practice doubling and also to develop representation and recording strategies. The Teachers' Notes page offers suggestions for implementation and discussion as well as ideas for extension and support.

This task is for students who know how to use base 10 blocks.

This task provides three types of comparison problems: Those with an unknown difference and two known numbers; those with a known difference and a bigger unknown number; and those with a known difference and smaller unknown number. Students may solve each type using addition or subtraction, although the language in specific problems tends to favor one approach over another.