This problem requires children to make sense of information and to work in a systematic way. The interactive is a machine with four colored lights, each corresponding to a rule regarding number properties. Students are to discover numbers that will satisfy all four rules and switch on all the lights. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support.

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.

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.

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).

This problem uses linking cubes as a concrete context for exploring simple multiplication and division, doubling, halves and quarters. The problem displays a rod of 4 cubes and asks students how many cubes are necessary to make rods related to it in a variety of ways. It can be used to introduce key concepts and vocabulary. The Teachers' Notes page offers suggestions for implementation, discussion questions, and ideas for extension and support.

This problem provides an opportunity for children to practice skip-counting and counting on. It lays a foundation for the concept of multiples and proportional thinking. Using linking cubes of two different colors, one color grouped in 2s and the other color grouped in 3s, children look for ways they can make a line of one color equal to a line of the other color. The Teachers' Notes page offers suggestions for implementation, discussion questions, and ideas for extension and support.

In this interactive game similar to Concentration(TM) students match fractions (1/2, 1/3, 3/4, and 5/9) to images that represent those fractions. This game can be played in pairs with the printed out cards or as a whole class on the interactive white board (IWB). This resource includes teacher notes with suggestions for introducing the game, discussion questions, support suggestions, a set of cards to be printed (PDF), a blank set of cards to make your own (PDF), and a full screen version of the game.

In this activity students apply their knowledge of triangle properties. It asks students to sort three types of triangles based on angle and side comparisons, while ignoring the size and orientation differences. Students can work online with an interactive Flash applet, or on a printed sheet (included). The Teachers' Notes page includes suggestions for implementation, discussion questions, and ideas for extension.

This data analysis activity requires students to read and interpret six written or graphical representations of data. Students must determine which graphs and analysis belong together. The data representations used include a pictograph, a circle graph, a frequency chart, a bar graph, and two written analyses including the terms mode, median, and mean for each data set. Included with the activity are teacher's notes, a hint, and the solution.

This brief article for young learners describes how ancient cultures developed units of measurement like the cubit and foot, and how estimation and precision play a role in measuring today. A printable page is available.

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.

This problem reinforces a learner's understanding of factors and multiples. Students are presented with the hundred grid or parts of the grid where specific numbers have been shaded and must find out which factors have been chosen in order to produce the shading. A link to a spreadsheet which shades the squares according to the chosen factors, can be used by students to check their hypotheses. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and ideas for extension and support.

The problems in this NRICH collection utilize simple mathematical concepts with an emphasis on the thinking process. These problems have been categorized by strategies and process skills with an aim at helping learners develop their mathematical thinking skills.

This problem provides an opportunity for students to practice counting and to represent and record findings in different ways: "Noah saw 12 legs walk by into the Ark. How many creatures did he see?" Multiple solution possibilities encourage students to be systematic in their strategies. The Teachers' Notes page offers suggestions for implementation, discussion questions, and an idea for extension.

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 the importance of developing a "sense of ten" as a foundation for place value and mental calculations. She suggests teaching strategies using ten-frames to promote this sense, including instructions for simple games. The article includes a list of references and a link to a related article, "Developing Early Number Sense" (cataloged separately).

This problem provides an opportunity for children to explore and visualize number patterns and sequences and to reinforce key number concepts and vocabulary such as odd and even, factors and multiples. Students cut consecutive number tracks into equal length pieces in several ways and investigate the patterns that emerge among the sums of the tracks. The Teachers' Notes page explains number tracks and offers suggestions for implementation, discussion questions, a printable sheet of number tracks (pdf), and ideas for extension and support.

In this activity students are asked to relate the numbers 1- 20 to rectangular shapes. Learners use unit squares or cubes to sort numbers by their 'shapes,' either squares, rectangles or sticks (rectangles of unit width). Ideas for implementation, extension and support are included.