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.

Unit 7: Rational Numbers
Lesson 9: Solutions of Inequalities

In this lesson, students consider situations where there might be more than one condition. Students have already learned “solution to an equation” to mean a value of the variable that makes the equation true. Here, they learn a similar definition about inequalities: a solution to an inequality is a value of the variable that makes the inequality true. But while the equations students solved in the last unit generally had one solution, the inequalities they solve in this unit have many, sometimes infinitely many, solutions.

Constraints in real-world situations reduce the range of possible solutions. Students reason abstractly by using inequalities or graphs of inequalities to represent those situations and interpreting the solutions, (MP2). Students think carefully about whether to include boundary values as solutions of inequalities in various contexts.

Unit 2: Introducing Ratios
Lesson 14: Solving Equivalent Ratio Problems

The purpose of this lesson is to give students further practice in solving equivalent ratio problems and introduce them to the info gap activity structure. The info gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for information they need to solve it. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6).

Unit 2: Introducing Ratios
Lesson 16: Solving More Ratio Problems

In this lesson, students use all representations they have learned in this unit—double number lines, tables, and tape diagrams—to solve ratio problems that involve the sum of the quantities in the ratio. They consider when each tool might be useful and preferable in a given situation and why (MP5). In so doing, they make sense of situations and representations, and are strategic in their choice of solution method (MP1).

Unit 3: Unit Rates and Percentages
Lesson 14: Solving Percentage Problems

In previous lessons, students saw that a percentage is a rate per 100. They were provided with double number line diagrams to develop this understanding and to solve problems involving percentages. In this lesson, students solve similar problems but with less support. Because double number lines are not provided, students have opportunities to choose approaches that seem appropriate. Drawing a double number line is still a good strategy, but students may opt for tables or even more abbreviated reasoning methods.

Unit 4: Dividing Fractions
Lesson 16: Solving Problems Involving Fractions

In this lesson, students use their understanding of and their facility with all four operations to represent and solve problems involving fractions. The last activity requires students to make sense of the problem and persevere in solving it (MP1).

Unit 3: Unit Rates and Percentages
Lesson 9: Solving Rate Problems

In previous lessons, students have used tables of equivalent ratios to reason about unit rates. In this lesson, students gain fluency working with unit rates without scaffolding (MP1). They choose what unit rate they want to use to solve a problem, divide to find the desired unit rate, and multiply or divide by the unit rate to answer questions. They may choose to create diagrams to represent the situations, but the problems do not prompt students to do so. The activity about which animal ran the farthest requires students to use multiple unit rates in a sequence to be able to convert all the measurements to the same unit.

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.

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.

Unit 8: Data Sets and Distributions
Lesson 2: Statistical Questions

In this lesson, students continue to analyze questions and the kinds of responses they can expect from those questions. They begin to recognize variability in data and learn about statistical questions and how they differ from non-statistical questions. In order to define variability, students categorize data sets and name the categories to make use of structure (MP7) because they are seeking mathematically important similarities between the objects.

Unit 6: Expressions and Equations
Lesson 3: Staying in Balance

The goal of this lesson is for students to understand that we can generally approach p+x=q by subtracting the same thing from each side and that we can generally approach px=q by dividing each side by the same thing. This is accomplished by considering what can be done to a hanger to keep it balanced.

Students are solving equations in this lesson in a different way than they did in the previous lessons. They are reasoning about things one could “do” to hangers while keeping them balanced alongside an equation that represents a hanger, so they are thinking about “doing” things to each side of an equation, rather than simply thinking “what value would make this equation true.”

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

Scholastic has produced a FREE website full of educational videos and step-by-step slides for students to work on. Study Jams focuses on science and mathematical concepts that are prevalent in 3rd, 4th, and 5th grade.

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.

Response to Intervention (RtI) has become a common support system for students; yet, no universal RtI model exists, especially for mathematics and specifically at the secondary level. This article focuses on a specific model for delivering Tier 2 mathematics supports and services at the secondary level: math labs. Evidence--based and research--supported interventions are discussed that support the delivery of Tier 2 services within a math lab secondary RtI structure. A fictionalized vignette, drawing from multiple actual cases, is presented to highlight the use of a Tier 2 math lab within a middle school setting.

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.