This Nrich game will help children to understand the tens and units structure of the numbers to a hundred. It can be used as an activity for one child on his/her own or by up to three at once. If there are four, it would be more suitable to play two parallel games.

This Nrich activity engages the pupils in both a spatial and numerical context. It gives them also the freedom to choose how they go about it - visualizing in their head, using paper, string etc. that they have requested and/or making use of a spreadsheet. They can learn a lot from adopting one method and then realizing that an alternative method would be better.

This Nrich task encourages creativity in developing patterns and using shapes to create composite shapes. This task could be done with tiles, blocks, or paper shapes.

Total solar eclipses are quite rare, so much so that they make the news when they do occur. This task explores some of the reasons why. Solving the problem is a good application of similar triangles

This short video and interactive assessment activity is designed to teach second graders about identifying and naming 3d figures.

This short video and interactive assessment activity is designed to teach third graders about identifying and naming 3d figures.

This lesson unit is intended to help teachers assess how well students are able to identify and use geometrical knowledge to solve a problem. In particular, this unit aims to identify and help students who have difficulty in: making a mathematical model of a geometrical situation; drawing diagrams to help with solving a problem; identifying similar triangles and using their properties to solve problems; and tracking and reviewing strategic decisions when problem-solving.

This Nrich activity can be used to build up children's confidence with the language associated with 2D shape.

This Nrich activity can be printed or used interactively. Students will write down and discuss similarities and differences they see.

This Nrich game offers an excellent opportunity to practice visualizing squares and angles on grids and also encourages students to look at strategies using systematic approaches. Describing strategies to others is always a good way to focus and clarify mathematical thought.

This short video and interactive assessment activity is designed to give fifth graders an overview of squares and rectangles.

Unit: Area and Surface Area
Lesson 17: Squares and Cubes

In this lesson, students learn about perfect squares and perfect cubes. They see that these names come from the areas of squares and the volumes of cubes with whole-number side lengths. Students find unknown side lengths of a square given the area or unknown edge lengths of a cube given the volume. To do this, they make use of the structure in expressions for area and volume (MP7).

Students also use exponents of 2 and 3 and see that in this geometric context, exponents help to efficiently express multiplication of the side lengths of squares and cubes. Students learn that expressions with exponents of 2 and 3 are called squares and cubes, and see the geometric motivation for this terminology. (The term “exponent” is deliberately not defined more generally at this time. Students will work with exponents in more depth in a later unit.)

In working with length, area, and volume throughout the lesson, students must attend to units. In order to write the formula for the volume of a cube, students look for and express regularity in repeated reasoning (MP8).

Note: Students will need to bring in a personal collection of 10–50 small objects ahead of time for the first lesson of the next unit. Examples include rocks, seashells, trading cards, or coins.

The whole idea of this Nrich problem is to invite children to picture something in their mind and in this instance, pupils will need to be familiar with properties of a cube. Ideally, it would be good to encourage your class to tackle this challenge purely by trying to imagine what is happening. To convince you and each other of their solutions, they will need to explain particularly carefully what they are picturing, which can be quite tricky, and you may find that they gesticulate rather a lot! In order to reach a joint conclusion, you might find it helpful to make a model of the cube from interlocking cubes.

Students learn that math is important in navigation and engineering. They learn about triangles and how they can help determine distances. Ancient land and sea navigators started with the most basic of navigation equations (speed x time = distance). Today, navigational satellites use equations that take into account the relative effects of space and time. However, even these high-tech wonders cannot be built without pure and simple math concepts — basic geometry and trigonometry — that have been used for thousands of years.

In this Nrich activity, student will work in groups and whole group to produce a data chart based on countable classroom situations.

An interactive applet and associated web page that demonstrate supplementary angles (two angles that add to 180 degrees.) The applet shows two angles which, while not adjacent, are drawn to strongly suggest visually that they add to a straight angle. Any point defining the angle scan be dragged, and as you do so, the other angle changes to remain supplementary to the one you change. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Unit: Area and Surface Area
Lesson 18: Surface Area of a Cube

In this lesson, students practice using exponents of 2 and 3 to express products and to write square and cubic units. Along the way, they look for and make use of structure in numerical expressions (MP7). They also look for and express regularity in repeated reasoning (MP8) to write the formula for the surface area of a cube. Students will continue this work later in the course, in the unit on expressions and equations.

Note: Students will need to bring in a personal collection of 10–50 small objects ahead of time for the first lesson of the next unit. Examples include rocks, seashells, trading cards, or coins.

After geometric series, this Nrich problem is one of the simplest infinite series with finite sum, all of whose terms are positive. This geometric demonstration of the result requires students to continue a pattern and to use several steps of reasoning to deduce that the sum is bounded by 2. Summing infinite geometric series also play an important role in the this proof, so this could be used to show an application of them in a larger proof. (It would be useful for students to be able to sum 12+14+18+⋯ before tackling this problem.)

In Nrich's Twisting and Turning, the Conway Rope Trick was introduced. You'll need to take a look at the video on that page and do the rope trick for yourself before reading the rest of this article, since here we're going to take a good long look at the symmetries of the resulting tangles.

This task presents a foundational result in geometry, presented with deliberately sparse guidance in order to allow a wide variety of approaches. Teachers should of course feel free to provide additional scaffolding to encourage solutions or thinking in one particular direction. We include three solutions which fall into two general approaches, one based on reference to previously-derived results (e.g., the Pythagorean Theorem), and another conducted in terms of the geometry of rigid transformations.