This Nrich problem is an accessible context in which pupils can apply their knowledge of number properties. It provides a great opportunity for learners to reason logically and to communicate their reasoning with others.

Unit 8: Data Sets and Distribution
Lesson 1: Got Data?

Students begin the unit by interacting closely with data. They collect data about themselves by measuring and answering survey questions, studying the different types of responses collected, and identifying the appropriate variables and units being measured.

Students learn about categorical and numerical data. They determine whether a particular survey question will produce one type of data or the other. They also get reacquainted with dot plots (often called line plots in earlier grades) as a way to represent data and make sense of what the data points mean in context (MP2).

EL Education has revised the workshop model to align with the Common Core instructional shifts, embed ongoing assessment to increase responsiveness to student needs, and help students develop self-reliance and perseverance. The first component in this revised workshop (Workshop 2.0) asks students to “grapple” independently with a problem or task. The second component is a collaborative opportunity for students to be metacognitive about their own approaches, justify their mathematical reasoning, and consider others’ mathematical reasoning and thinking.

The Starfall greater than, less than, equal to game is a great option for number comparison, counting, and number identification in a steady, consistent format. This game is a great option for independent center practice, whole group instruction, or small group instruction.

This Nrich problem follows on from Keep It Simple and Egyptian Fractions
These three problems together offer students an opportunity to engage with some mathematical ideas in depth and not just with the rather mechanical process of adding and subtracting fractions.

This problem in particular requires students to compare fractions and may deepen their understanding of their relative sizes.

This Nrich problem requires children to apply their knowledge of factors and multiples, and is a good way of making the link between sharing, division and multiples/factors. It may also be used to introduce learners to the fact that a problem can have more than one solution and that the solutions can be generalized. It can be approached in many different ways so can be a useful context in which to talk about different ways of recording and different methods of solving problems.

This Nrich task is a group activity or game. Students work to discover a rule by working together to evaluate patterns.

This is the story of how Les Paul created the world's first solid-body electric guitar, countless other inventions that changed modern music, and one truly epic career in rock and roll. How to make a microphone? A broomstick, a cinderblock, a telephone, a radio. How to make an electric guitar? A record player's arm, a speaker, some tape. How to make a legendary inventor? A few tools, a lot of curiosity, and an endless faith in what is possible, this unforgettable biography will resonate with inventive readers young and old.

This lesson uses GoMath Chapter 12 Lesson 6 resources and incorporates supplemental digital resources to reinforce lesson objectives.

This Nrich problem provides a fraction-based challenge for students who already possess a good understanding of fraction addition and subtraction, and it leads to algebraic manipulation of that same process.

Meet savvy scientist and inventor Hedy Lamarr, also known for her career as a glamorous international movie star. Dubbed "The Most Beautiful Woman in the World," Hedy actually preferred spending time creating inventions in her workshop to strutting down the red carpet. Hedy co-invented the technology known as frequency hopping, which turned out to be one of the most important scientific breakthroughs of the twentieth century! Today's cell phone, computers, and other electronic devices would be more vulnerable to hacking without the groundbreaking system discovered by a world-famous actress and gifted inventor. 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: Create small groups. Pass out one of the challenges listed in the lesson plan/book card to each group for them to come up with an invention that will solve the problem at hand.

Unit 8: Data Sets and Distributions
Lesson 6: Histograms

In this lesson students are introduced to histograms. They learn that, like a dot plot, a histogram can be used to show the distribution of a numerical data set, but unlike a dot plot, a histogram shows the frequencies of groups of values, rather than individual values. Students analyze the structures of dot plots and histograms displaying the same data sets and determine what information is easier to to understand from each type of display (MP7). Students read and interpret histograms in context (MP2) to prepare them to create a histogram.

This Nrich task gives opportunities for pupils to explore, to discover, to analyze and communicate. It's a real catalyst for pupils' curiosity. It allows pupils to approach it in whatever way they find most helpful. It also provides opportunities for using and extending visualizing skills. The activity also opens out the possibility of pupils asking “I wonder what would happen if . . .?” showing their resilience and perseverance.

Frances Gabe detested housework, so she invented a contraption to free herself from this tedious task forever: a self-cleaning house! Gabe's wacky, wonderful home included almost 70 new patented inventions, from a soap-spraying sprinkler in the ceiling to a kitchen cabinet that washed, dried, and stored dishes all in one place. Though Gabe's invention didn't catch on, her determination and clever thinking remind us that we don't have to accept the world as it is; we can improve it using our minds and our own two hands. 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: Frances Gabe created over 70 inventions because she hated cleaning. What is one thing you hate doing for chores? Develop an invention to have it clean itself.

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

Unit 9: Putting It All Together
Lesson 4: How Do We Choose?

This lesson is optional. This is the first of three lessons that explore the mathematics of voting: democratic processes for making decisions. The activities in these lesson build on each other. Doing all of the activities in the three lessons would take more than three class periods—possibly as many as five. It is up to the teacher how much time to spend on this topic. It is not necessary to do the entire set of activities to get some benefit from them, although more connections are made the farther one gets. As with all lessons in this unit, all related standards have been addressed in prior units; this lesson provides an optional opportunity to go more deeply and make connections between domains.

The activities in this lesson are about voting on issues where there are two choices. Students use proportional reasoning concepts and skills developed in grade 6 to compare voting results of two groups, to determine whether an issue wins an election with a supermajority rule, and discover that a few people can determine the results of an election when very few people vote.

Most of the activities use students’ skills from earlier units to reason about ratios and proportional relationships (MP2) in the context of real-world problems (MP4). While some of the activities do not involve much computation, they all require serious thinking. In many activities, students have to make choices of how to assign votes and justify their methods (MP3).

Most importantly, this lesson addresses topics that are important for citizens in a democracy to understand. Teachers may wish to collaborate with a civics or government teacher to learn how the fictional middle-school situations in this lesson relate to real-world elections.

Division is a building block of math. This tutorial shows you how to perform long division by going through the process one step at a time.

Understanding place value is a building block of understanding numbers. Follow along with this tutorial to see how to find the value of a digit for a given number!

To add numbers, you can line up the numbers vertically and then add the matching places together. This tutorial shows you how to add numbers vertically!

This Nrich low threshold high ceiling task is accessible to everyone. It gives children the chance to share the way they picture (visualize) numbers and their methods of counting. One of the key features of this task is that it can be interpreted differently, depending on the image, so that children can decide for themselves whether they are counting individual fruit, cartons of fruit... Therefore there may also be an opportunity for children to develop their estimation skills as well as appreciating different ways of counting.

Unit 4: Dividing Fractions
Lesson 4: How Many Groups? (Part 1)

This lesson and the next one extend the “how many groups?” interpretation of division to situations where the “group” can be fractional. This builds on the work in earlier grades on dividing whole numbers by unit fractions.

Students use pattern blocks to answer questions about how many times a fraction goes into another number (e.g., how many 2/3s are in 2?), and to represent multiplication and division equations involving fractions. In this lesson, they focus on situations where the quotient (the number of groups) is a whole number.

This lesson is the first in a group of six lessons that trace out a gradual progression of learning—from reasoning with specific quantities, to using a symbolic formula for division of fractions (MP8).