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).

This problem provides an opportunity for students to form and test conjectures, and make generalizations, while exploring the effect of parity on simple whole number sums. Solvers are asked to arrange given sets of numbers in a V formation so that the sums of the numbers in each "arm" are equal. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, a printable record sheet (pdf) and links to two YouTube videos demonstrating use of the problem in a professional development setting (videos cataloged separately).

The purpose of this task is for students to find different pairs of numbers that sum to 9.

This task requires students to study the make-a-ten strategy that they should already know and use intuitively. In this strategy, knowledge of which sums make a ten, together with some of the properties of addition and subtraction, are used to evaluate sums which are larger than 10.

Making a 10 provides a technique to help students master single digit addition. The task is designed to help students visualize where the 10's are on a single digit addition table and explain why this is so. This knowledge can then be used to help them learn the addition table.

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.

Find strategies and activities that you can use in the classroom that tie directly to the Early learning Preschool core standards.

In this Cyberchase video segment, the CyberSquad helps resolve a dispute about the squares on the Gollywood Walk of Fame.

This activity is a good way of introducing the value of algebraic notation and translating verbal expressions to algebraic expressions. Students are asked "to think of a number," then to do seven consecutive computational steps beginning with their number and to figure out why 2 is always the final result. The teacher's notes, hints, and solution are provided.

Find resources from NAEYC on how to have playful math learning in school, how children learn and understand math, math ideas for families, and more.

The National Council of Teachers of Mathematics advocates for high-quality mathematics teaching and learning for each and every student. Find research and resources related to preschool here.

This web page provides instructions for a basic form of Nim, an ancient game that develops strategic thinking. Starting with a total of 7 counters, two players take turns removing one or two at a time. The player who takes the last counter wins. The game of Nim is very adaptable. This page includes questions that encourage players to generalize a winning strategy as well as a link to another page describing several of variations.

This activity promotes algebraic thinking of equivalency as well as giving children practice in addition and subtraction. Students see weights on each side of a balance, and are asked to find ways they can hang a weight or two weights to balance the bar. An interactive balance allows student to explore the different ways weights can be added to balance or equalize the bars. A more challenging problem,"Getting the Balance" is cataloged separately. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support.

This activity helps children become more familiar with horizontal and vertical number lines (0 through 10) and how to use them for addition. It can be used to introduce subtraction as the inverse of addition and the use of an unknown number. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, printable number lines (pdf), and a link to a related game, Incey Wincey Spider (catalogued separately).

The author of this one-page article discusses early number sense and how it develops. She provides research background and suggests teaching strategies that promote early number sense, including instructions for simple games using dot cards. The article includes a list of references and a link to a follow-up article, "A Sense of 'ten' and Place Value" (cataloged separately).

This number puzzle helps children develop fluency with pairs of numbers that sum to 10 while applying logic and spatial-visualization skills. Users arrange 9 small triangles within a large one so that the numbers on the matching edges total 10. Students can use the interactive Flash applet or the printable (pdf) triangles provided. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and a link to related games (cataloged separately).

This task acts as a bridge between understanding place value and using strategies based on place value for addition and subtraction.

Open Middle tasks provide opportunities for student to approach a mathematical task using different strategies and representations. They can be used as a warm-up/closing activity, as a formative assessment, or to facilitate discourse and discussion and get insite into student thinking and problem solving. These tasks provide a great opportunity for student to engage with the Standards for Mathematical Practice.