Sarah E. Goode was one of the first African-American women to get a US patent. Working in her furniture store, she recognized a need for a multi-use bed and through hard work, ingenuity, and determination, invented her unique cupboard bed. She built more than a piece of furniture. She built a life far away from slavery, a life where her sweet dreams could come true. 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: Your school has had an influx of new students and every class seems to be bursting at the seams! You have an additional 10 students just in your classroom alone. Because of this limited space, your school is looking for solutions. They decided that every student is going to get a new desk and chair, but it’s going to be PORTABLE. That way, you can take your desk & chair with you wherever you might go.

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

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.

Unit 2: Introducing Ratios
Lesson 13: Tables and Double Number Line Diagrams

In this lesson, students explicitly connect and contrast double number lines and tables. They also encounter a problem involving relatively small fractions, so the flexibility of a table makes it preferable to a double number line. Students have used tables in earlier grades to identify arithmetic patterns and record measurement equivalents. In grade 6, a new feature of working with tables is considering the relationship between values in different rows. Two features of tables make them more flexible than double number lines:

On a double number line, differences between numbers are represented by lengths on each number line. While this feature can help support reasoning about relative sizes, it can be a limitation when large or small numbers are involved, which may consequently hinder problem solving. A table removes this limitation because differences between numbers are no longer represented by the geometry of a number line.
A double number line dictates the ordering of the values on the line, but in a table, pairs of values can be written in any order. 5 pounds of coffee cost $40. How much does 8.5 pounds cost?

At this point in the unit, students should have a strong sense of what it means for two ratios to be equivalent, so they can fill in a table of equivalent ratios with understanding instead of just by following a procedure. Students can also always fall back to other representations if needed.

In this activity, learners explore center of gravity, or balance point, of stacked blocks. Simple wooden blocks can be stacked so that the top block extends completely past the end of the bottom block, seemingly in a dramatic defiance of gravity. A mathematical pattern can be noted in the stacking.

This learning video presents an introduction to graph theory through two fun, puzzle-like problems: ''The Seven Bridges of Konigsberg'' and ''The Chinese Postman Problem''. Any high school student in a college-preparatory math class should be able to participate in this lesson. Materials needed include: pen and paper for the students; if possible, printed-out copies of the graphs and image that are used in the module; and a blackboard or equivalent. During this video lesson, students will learn graph theory by finding a route through a city/town/village without crossing the same path twice. They will also learn to determine the length of the shortest route that covers all the roads in a city/town/village. To achieve these two learning objectives, they will use nodes and arcs to create a graph and represent a real problem.

Unit 6: Expressions and Equations
Lesson 1: Tape Diagrams and Equations

The purpose of this lesson is to help students remember from earlier grades how tape diagrams can be used to represent operations. There are two roles that tape diagrams (or any diagrams) can play: helping to visualize a relationship, and helping to solve a problem. The focus here is the first of these, so that later students can use diagrams for the second of these. In this lesson, students both interpret tape diagrams and create their own.

Note that the terms “solution” and “variable” aren’t defined until the next lesson, nor should any solution methods be generalized yet. Students should engage with the activities and reason about unknown quantities in ways that make sense to them.

The Institute of Education Sciences (IES) publishes practice guides in education to bring the best
available evidence and expertise to bear on current challenges in education. Authors of practice
guides combine their expertise with the findings of rigorous research, when available, to develop
specific recommendations for addressing these challenges. The authors rate the strength of the
research evidence supporting each of their recommendations. See Appendix A for a full description
of practice guides.
The goal of this practice guide is to offer educators specific, evidence-based recommendations
that address the challenge of teaching early math to children ages 3 to 6. The guide provides
practical, clear information on critical topics related to teaching early math and is based on the
best available evidence as judged by the authors.
Practice guides published by IES are available on our website at http://whatworks.ed.gov.

Doing this Nrich problem is an excellent way to work at problem solving with learners. The problem lends itself to small group work, and provides an engaging context for pupils to use the skills of trial and error, and working systematically.

Students will be able to calculate the number of dots needed to make ten by looking at the ten frame flashcard.

n this online game, Ten Frame Mania by Greg Tang, students make a given number in a digital ten frame to win the game for numbers up to 20. Thinking about numbers using frames of 10 can be a helpful way to learn basic number facts.

This Nrich problem offers an excellent opportunity for students to practice converting fractions into decimals, while also investigating a wider question that connects their knowledge of prime factors and place value.

This Nrich activity gives children the opportunity to use, reinforce and extend their knowledge of place value, multiples and times tables. It enables them to use their understanding of pattern and possibly their visualizing skills. This activity also offers an opportunity to discuss the strategies the children come up with - what is a good strategy for putting the number tiles back in the correct places as quickly as possible? What makes one strategy 'smarter' than another?

Students explore combinations in this Nrich activity. There is a simulator to help students with visualizing the possible outcomes. Discussion is a key element.

This Nrich problem encourages children to explain observations and to generalize. It requires a good understanding of multiplication. It may also introduce the idea that opposite faces of a dice add to seven, if that is something with which learners are not already familiar

This Nrich problem supports the development of the idea of generic proof with the children. This is a tricky concept to grasp but it draws attention to mathematical structures that are not often addressed at primary school level.

At a time when most African Americans were slaves, Benjamin Banneker was born free in 1731. Known and admired for his work in science, mathematics, and astronomy, he built a strike clock based on his own drawings and using a pocket-knife at the age of 22. 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: Find a discarded object that can be taken apart. Take apart the item and make your own Things Come Apart arrangement.

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

There are fascinating patterns to be found in recurring decimals. This Nrich problem explores the relationship between fraction and decimal representations. It's a great opportunity to practice converting fractions to decimals with and without a calculator.