Unit 6: Expressions and Equations
Lesson 7: Revisit Percentages

Students learned about what percentages are and how to solve certain problems in an earlier unit. At the time, they did not learn an efficient procedure for finding B in “A% of B is C” given A and C, because they didn't have an efficient way to solve an equation of the form px=q. Now they do, so we briefly revisit this type of problem.

Students will use the Rhythm experiment on Google's Musiclab Chrome Music Lab to create a rhythm. Students will then use the rhythm they created to write three fraction questions and answer them.

This Nrich problem appears at first to be about angles and rotations, but as students explore more deeply, they may be surprised to discover links to factors, multiples and primes. The images and interactivity provide an enticing hook to stimulate students' curiosity.

Students use a variety of properties concerning circles and sectors to justify statements.

This Nrich activity provides a meaningful task for practicing rounding two-digit numbers to the nearest multiple of 10. It encourages children to record their results, notice patterns and make predictions.

In this NRich activity students will analyze a pattern on a coordinate plane in order to make predictions.

This Nrich problem lets you spot misconceptions your students have about subtraction and division of fractions, while giving students an opportunity to practice the procedures in an intriguing context - students' curiosity will be raised by the strange patterns in the calculations, and we hope they will yearn to explain what is happening.

This Nrich problem is a good opportunity to encourage children to have a system for finding all possible solutions. It is also an ideal context in which to help children deepen their understanding of factors and multiples in a playful environment.

This Nrich activity will be very useful when wishing to challenge and extend pupils' spatial awareness with 2D shapes. It can also be an exercise in perseverance.

Unit 1: Scale Drawings
Lesson 4: Scaled Relationships

In previous lessons, students looked at the relationship between a figure and a scaled copy by finding the scale factor that relates the side lengths and by using tracing paper to compare the angles. This lesson takes both of these comparisons a step further.

Students study corresponding distances between points that are not connected by segments, in both scaled and unscaled copies. They notice that when a figure is a scaled copy of another, corresponding distances that are not connected by a segment are also related by the same scale factor as corresponding sides.
Students use protractors to test their observations about corresponding angles. They verify in several sets of examples that corresponding angles in a figure and its scaled copies are the same size.
Students use both insights—about angles and distances between points—to make a case for whether a figure is or is not a scaled copy of another (MP3). Practice with the use of protractors will help develop a sense for measurement accuracy, and how to draw conclusions from said measurements, when determining whether or not two angles are the same.

The Mathematics Vision Project (MVP) curriculum has been developed to realize the vision and goals of the New Core Standards of Mathematics. The Comprehensive Mathematics Instruction (CMI) framework is an integral part of the materials. You can read more about the CMI framework in the Utah Mathematics Teacher Journal. (UCTM, 2009)

New York City in the 1860s was a mess: crowded, disgusting, filled with garbage. You see, way back in 1860, there were no subways, just cobblestone streets. That is, until Alfred Ely Beach had the idea for a fan-powered train that would travel underground. On February 26, 1870, after fifty-eight days of drilling and painting and plastering, Beach unveiled his masterpiece—and throngs of visitors took turns swooshing down the track. The resource includes a lesson plan/book card, a design challenge, and copy of a design thinking journal that provide guidance on using the book to inspire students' curiosity for design thinking. Maker Challenge: Think about the way most people in your community travel. Invent a new way of traveling around your community that takes into account the following: helpful to the community, economical to those who use it, convenient for users. What would your new travel system look like? Sketch a new design, and then create a physical prototype of the new design to scale. Keep in mind: Where the system travels, how it is powered, why it is helpful to the community, and any features that make it special.

A document is included in the resources folder that lists the complete standards-alignment for this book activity.

Unit 7: Rational Numbers
Lesson 15: Shapes on the Coordinate Plane

In this lesson, students apply their understanding of rational coordinates and distance in the coordinate plane to construct polygons and navigate a maze. Students plot coordinates in all four quadrants and find horizontal and vertical distances.

This Nrich game can give pupils the opportunity to use their number knowledge and it can be adapted to stretch even the highest attainers. In its simplest form it can be accessed by anyone in the class who is able to connect the number of spots on a die to the numeral that represents it. Altering the rules and including operations will give the children opportunities to explore ideas about what makes a "good" game and to develop winning strategies to play their games.

An interactive applet and associated web page that demonstrate the concept of similar polygons. Applets show that polygons are similar if the are the same shape and possibly rotated, or reflected. In each case the user can drag one polygons and see how another polygons changes to remain similar to it. The web page describes all this and has links to other related pages. 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.

The topic of music can make a good connection between science and mathematics
The nature of sound and the working of the ear are rich areas of applied mathematics.
The ratio emphasis follows from harmonics or overtones and rests on ideas like lowest common multiple.

Unit 4: Dividing Fractions
Lesson 1: Size of Divisor and Size of Quotient

The first three lessons of this unit help students make sense of division situations. In this opening lesson, students begin thinking about the relationships between the numbers in a division equation. They see that they can estimate the size of the quotient by reasoning about the relative sizes of the divisor and the dividend.

Students begin exploring these relationships in concrete situations. For example, they estimate how many thinner and thicker objects are needed to make a stack of a given height, and how many segments of a certain size make a particular length.

Later, they generalize their observations to division expressions (MP7). Students become aware that dividing by a number that is much smaller than the dividend results in a quotient that is larger than 1, that dividing by a number that is much larger than the dividend gives a quotient that is close to 0, and that dividing by a number that is close to the dividend results in a quotient that is close to 1.

Students will learn how to skip count by watching videos, using number charts, and playing educational computer games.

An interactive applet and associated web page that demonstrate the slope (m) of a line. The applet has two points that define a line. As the user drags either point it continuously recalculates the slope. The rise and run are drawn to show the two elements used in the calculation. The grid, axis pointers and coordinates can be turned on and off. The slope calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the concept of slope, a worked example and has links to other pages relating to coordinate geometry. 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.

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.