This lesson unit is intended to help teachers assess how well students are able to: Understand conditional probability; represent events as a subset of a sample space using tables and tree diagrams; and communicate their reasoning clearly.

This lesson unit is intended to help you assess how well students are able to: recognize and use common 2D representations of 3D objects and identify and use the appropriate formula for finding the circumference of a circle.

This lesson unit is intended to help you assess how well students are able to: interpret a situation and represent the variables mathematically; select appropriate mathematical methods; interpret and evaluate the data generated; and communicate their reasoning clearly.

This task was developed by high school and postsecondary mathematics and design/pre-construction educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

This lesson unit is intended to help you assess how well students are able to: solve simple problems involving ratio and direct proportion; choose an appropriate sampling method; and collect discrete data and record them using a frequency table.

This lesson unit is intended to help teachers assess how well students are able to: form and solve linear equations involving factorizing and using the distributive law. In particular, this unit aims to help teachers identify and assist students who have difficulties in: using variables to represent quantities in a real-world or mathematical problem and solving word problems leading to equations of the form px + q = r and p(x + q) = r.

This lesson unit is intended to help teachers assess how well students are able to classify solutions to a pair of linear equations by considering their graphical representations. In particular, this unit aims to help teachers identify and assist students who have difficulties in: using substitution to complete a table of values for a linear equation; identifying a linear equation from a given table of values; and graphing and solving linear equations.

In this unit, students will read and interpret primary sources to address the question “How do we measure the attainment of human rights?” By exploring the Universal Declaration of Human Rights, the UN’s Guide to Indicators of Human Rights, and data about development indicators from multiple databases, students will unpack the complexities of using indicators to measure human rights.

This lesson unit is intended to help you assess how well students are able to: Calculate the mean, median, mode, and range from a frequency chart; and to use a frequency chart to describe a possible data set, given information on the mean, median, mode, and range.

This lesson unit is intended to help teahcers assess how well students are able to interpret speed as the slope of a linear graph and translate between the equation of a line and its graphical representation.

This lesson unit is intended to help teachers assess how well students are able to understand and use directed numbers in context. It is intended to help identify and aid students who have difficulties in ordering, comparing, adding, and subtracting positive and negative integers. Particular attention is paid to the use of negative numbers on number lines to explore the structures: starting temperature + change in temperature = final temperature final temperature Đ change in temperature = starting temperature final temperature Đ starting temperature = change in temperature.

This lesson unit is intended to help you assess how well students use algebra in context, and in particular, how well students: explore relationships between variables in everyday situations; find unknown values from known values; find relationships between pairs of unknowns, and express these as tables and graphs; and find general relationships between several variables, and express these in different ways by rearranging formulae.

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 lesson unit is intended to help teachers assess how well students are able to: interpret a situation and represent the variables mathematically; select appropriate mathematical methods to use; explore the effects of systematically varying the constraints; interpret and evaluate the data generated and identify the break-even point, checking it for confirmation; and communicate their reasoning clearly.

This lesson unit is intended to help assess how well students are able to interpret and use scale drawings to plan a garden layout. This involves using proportional reasoning and metric units.

This lesson unit is intended to help you assess how well students are able to: Model a situation; make sensible, realistic assumptions and estimates; and use assumptions and estimates to create a chain of reasoning, in order to solve a practical problem.

This lesson unit is intended to help you assess how well students are able to: Interpret a situation and represent the variables mathematically; select appropriate mathematical methods to use; explore the effects on the area of a rectangle of systematically varying the dimensions whilst keeping the perimeter constant; interpret and evaluate the data generated and identify the optimum case; and communicate their reasoning clearly.

This lesson unit is intended to help sixth grade teachers assess how well students are able to: Analyze a realistic situation mathematically; construct sight lines to decide which areas of a room are visible or hidden from a camera; find and compare areas of triangles and quadrilaterals; and calculate and compare percentages and/or fractions of areas.

Rational Numbers

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Solve problems with positive rational numbers.
Plot positive rational numbers on a number line.
Understand the equal sign.
Use the greater than and less than symbols with positive numbers (not variables) and understand their relative positions on a number line.
Recognize the first quadrant of the coordinate plane.

Lesson Flow

The first part of this unit builds on the prerequisite skills needed to develop the concept of negative numbers, the opposites of numbers, and absolute value. The unit starts with a real-world application that uses negative numbers so that students understand the need for them. The unit then introduces the idea of the opposite of a number and its absolute value and compares the difference in the definitions. The number line and positions of numbers on the number line is at the heart of the unit, including comparing positions with less than or greater than symbols.

The second part of the unit deals with the coordinate plane and extends student knowledge to all four quadrants. Students graph geometric figures on the coordinate plane and do initial calculations of distances that are a straight line. Students conclude the unit by investigating the reflections of figures across the x- and y-axes on the coordinate plane.

Getting Started

Type of Unit: Introduction

Prior Knowledge

Students should be able to:

Understand ratio concepts and use ratios.
Use ratio and rate reasoning to solve real-world problems.
Identify and use the multiplication property of equality.

Lesson Flow

This unit introduces students to the routines that build a successful classroom math community, and it introduces the basic features of the digital course that students will use throughout the year.

An introductory card sort activity matches students with their partner for the week. Then over the course of the week, students learn about the routines of Opening, Work Time, Ways of Thinking, Apply the Learning (some lessons), Summary of the Math, Reflection, and Exercises. Students learn how to present their work to the class, the importance of students’ taking responsibility for their own learning, and how to effectively participate in the classroom math community.

Students then work on Gallery problems, to further explore the resources and tools and to learn how to organize their work.

The mathematical work of the unit focuses on ratios and rates, including card sort activities in which students identify equivalent ratios and match different representations of an equivalent ratio. Students use the multiplication property of equality to justify solutions to real-world ratio problems.

This lesson unit is intended to help teachers assess how well students are able to solve quadratics in one variable. In particular, the lesson will help teachers identify and help students who have the following difficulties: making sense of a real life situation and deciding on the math to apply to the problem; solving quadratic equations by taking square roots, completing the square, using the quadratic formula, and factoring; and interpreting results in the context of a real life situation.

In Module 3, students' understanding of addition and subtraction of fractions extends from earlier work with fraction equivalence and decimals. This module marks a significant shift away from the elementary grades' centrality of base ten units to the study and use of the full set of fractional units from Grade 5 forward, especially as applied to algebra.

Mathematically Productive Instructional Routines (MPIR) are short (10ish minutes), daily exercises aimed at building number sense. These six different MPIR are part of the Mathematically Productive Instructional Routines collection from the Washington Office of Public Instruction and the Washington Association of Educational Service Districts.

Getting Started

Type of Unit: Introduction

Prior Knowledge

Students should be able to:

Solve and write numerical equations for whole number addition, subtraction, multiplication, and division problems.
Use parentheses to evaluate numerical expressions.
Identify and use the properties of operations.

Lesson Flow

In this unit, students are introduced to the rituals and routines that build a successful classroom math community and they are introduced to the basic features of the digital course that they will use throughout the year.

An introductory card sort activity matches students with their partner for the week. Then over the course of the week, students learn about the lesson routines: Opening, Work Time, Ways of Thinking, Apply the Learning, Summary of the Math, and Reflection. Students learn how to present their work to the class, the importance of taking responsibility for their own learning, and how to effectively participate in the classroom math community.

Students then work on Gallery problems to further explore the program’s technology resources and tools and learn how to organize their work.

The mathematical work of the unit focuses on numerical expressions, including card sort activities in which students identify equivalent expressions and match an expression card to a word card that describes its meaning. Students use the properties of operations to identify equivalent expressions and to find unknown values in equations.

Fractions and Decimals

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Multiply and divide whole numbers and decimals.
Multiply a fraction by a whole number.
Multiply a fraction by another fraction.
Write fractions in equivalent forms, including converting between improper fractions and mixed numbers.
Understand the meaning and structure of decimal numbers.

Lesson Flow

This unit extends students’ learning from Grade 5 about operations with fractions and decimals.

The first lesson informally introduces the idea of dividing a fraction by a fraction. Students are challenged to figure out how many times a 14-cup measuring cup must be filled to measure the ingredients in a recipe. Students use a variety of methods, including adding 14 repeatedly until the sum is the desired amount, and drawing a model. In Lesson 2, students focus on dividing a fraction by a whole number. They make a model of the fraction—an area model, bar model, number line, or some other model—and then divide the model into whole numbers of groups. Students also work without a model by looking at the inverse relationship between division and multiplication. Students explore methods for dividing a whole number by a fraction in Lesson 3, for dividing a fraction by a unit fraction in Lesson 4, and for dividing a fraction by another fraction in Lesson 6. Students examine several methods and models for solving such problems, and use models to solve similar problems.

Students apply their learning to real-world contexts in Lesson 6 as they solve word problems that require dividing and multiplying mixed numbers. Lesson 7 is a Gallery lesson in which students choose from a number of problems that reinforce their learning from the previous lessons.

Students review the standard long-division algorithm for dividing whole numbers in Lesson 8. They discuss the different ways that an answer to a whole number division problem can be expressed (as a whole number plus a remainder, as a mixed number, or as a decimal). Students then solve a series of real-world problems that require the same whole number division operation, but have different answers because of how the remainder is interpreted.

Students focus on decimal operations in Lessons 9 and 10. In Lesson 9, they review addition, subtraction, multiplication, and division with decimals. They solve decimal problems using mental math, and then work on a card sort activity in which they must match problems with diagram and solution cards. In Lesson 10, students review the algorithms for the four basic decimal operations, and use estimation or other methods to place the decimal points in products and quotients. They solve multistep word problems involving decimal operations.

In Lesson 11, students explore whether multiplication always results in a greater number and whether division always results in a smaller number. They work on a Self Check problem in which they apply what they have learned to a real-world problem. Students consolidate their learning in Lesson 12 by critiquing and improving their work on the Self Check problem from the previous lesson. The unit ends with a second set of Gallery problems that students complete over two lessons.

Expressions

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Write and evaluate simple expressions that record calculations with numbers.
Use parentheses, brackets, or braces in numerical expressions and evaluate expressions with these symbols.
Interpret numerical expressions without evaluating them.

Lesson Flow

Students learn to write and evaluate numerical expressions involving the four basic arithmetic operations and whole-number exponents. In specific contexts, they create and interpret numerical expressions and evaluate them. Then students move on to algebraic expressions, in which letters stand for numbers. In specific contexts, students simplify algebraic expressions and evaluate them for given values of the variables. Students learn about and use the vocabulary of algebraic expressions. Then they identify equivalent expressions and apply properties of operations, such as the distributive property, to generate equivalent expressions. Finally, students use geometric models to explore greatest common factors and least common multiples.

Equations and Inequalities

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Add, subtract, multiply, and divide with whole numbers, fractions, and decimals.
Use the symbols <, >, and =.
Evaluate expressions for specific values of their variables.
Identify when two expressions are equivalent.
Simplify expressions using the distributive property and by combining like terms.
Use ratio and rate reasoning to solve real-world problems.
Order rational numbers.
Represent rational numbers on a number line.

Lesson Flow

In the exploratory lesson, students use a balance scale to find a counterfeit coin that weighs less than the genuine coins. Then continuing with a balance scale, students write mathematical equations and inequalities, identify numbers that are, or are not, solutions to an equation or an inequality, and learn how to use the addition and multiplication properties of equality to solve equations. Students then learn how to use equations to solve word problems, including word problems that can be solved by writing a proportion. Finally, students connect inequalities and their graphs to real-world situations.

Rate

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Solve problems involving all four operations with rational numbers.
Understand quantity as a number used with a unit of measurement.
Solve problems involving quantities such as distances, intervals of time, liquid volumes, masses of objects, and money, and with the units of measurement for these quantities.
Understand that a ratio is a comparison of two quantities.
Write ratios for problem situations.
Make and interpret tables, graphs, and diagrams.
Write and solve equations to represent problem situations.

Lesson Flow

In this unit, students will explore the concept of rate in a variety of contexts: beats per minute, unit prices, fuel efficiency of a car, population density, speed, and conversion factors. Students will write and refine their own definition for rate and then use it to recognize rates in different situations. Students will learn that every rate is paired with an inverse rate that is a measure of the same relationship. Students will figure out the logic of how units are used with rates. Then students will represent quantitative relationships involving rates, using tables, graphs, double number lines, and formulas, and they will see how to create one such representation when given another.

Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset.

Students will calculate the glide slope ratio and angle of paper airplanes they have created. They will make claims about the type of airplane and support claims with evidence and reasoning from their class data.

This resource provides students with the opportunity to solve a multi-step contextual word problem with a degree of difficulty appropriate to Grade 4, requiring application of knowledge and skills.

The Fifth Grade Elementary Framework for Science and Integrated Subjects,Earth and Space: Patterns in the Sky, uses the phenomena of perceived sun and moon movements that seem to move around the Earth to explore stars, Earth orbit and rotation and moon orbit around Earth.  It is part of Elementary Framework for Science and Integrated Subjects project, a statewide Clime Time collaboration among ESD 123, ESD 105, North Central ESD, and the Office of Superintendent of Public Instruction. Development of the resources is in response to a need for research- based science lessons for elementary teachers that are integrated with English language arts, mathematics and other subjects such as social studies. The template for Elementary Science and Integrated Subjects  can serve as an organized, coherent and research-based roadmap for teachers in the development of their own NGSS aligned science lessons.  Lessons can also be useful for classrooms that have no adopted curriculum as well as to serve as enhancements for  current science curriculum. The EFSIS project brings together grade level teams of teachers to develop lessons or suites of lessons that are 1) pnenomena based, focused on grade level Performance Expectations, and 2) leverage ELA and Mathematics Washington State Learning Standards.

Learn to connect position-time and velocity-time graphs. Explore velocity using an animated car icon connected to either a position-time or a velocity-time graph, or both. Then investigate other motion graphs.

This resource is an integrated unit spanning math, economics and English. This unit is focused on the the subject of the minimum wage and the themes of equity, financial stability and quality of life.

How does energy flow in and out of our atmosphere? Explore how solar and infrared radiation enters and exits the atmosphere with an interactive model. Control the amounts of carbon dioxide and clouds present in the model and learn how these factors can influence global temperature. Record results using snapshots of the model in the virtual lab notebook where you can annotate your observations.

Explore how the Earth's atmosphere affects the energy balance between incoming and outgoing radiation. Using an interactive model, adjust realistic parameters such as how many clouds are present or how much carbon dioxide is in the air, and watch how these factors affect the global temperature.

In this activity, kids will work on two fundamental early math skills – sorting/classifying, and graphing. There will also be some great fine motor skill practice! Includes place-based discussion questions, activity instructions, extension activities, songs, and student graph worksheets.

NGSS: K-LS1-1, 1-LS1-1, partially meets K-ESS3-1 (book and discussion)

Common Core: MP.4

Time: 45 minutes

Matierals: bag of dried beans ("16 bean soup"), paper bowls, glue, chart paper, the book "One Bean" or similar book about growing food plants, especially beans.

Use a series of interactive models and games to explore electrostatics. Learn about the effects positive and negative charges have on one another, and investigate these effects further through games. Learn about Coulomb's law and the concept that both the distance between the charges and the difference in the charges affect the strength of the force. Explore polarization at an atomic level, and learn how a material that does not hold any net charge can be attracted to a charged object. Students will be able to: