This lesson unit is intended to help teachers assess how well students are able to create and solve linear equations. In particular, the lesson will help you identify and help students who have the following difficulties: solving equations with one variable and solving linear equations in more than one way.

This Java applet activity allows students to explore the various situations described in "The Chairs Around the Table" lesson (cataloged separately). The user can select Exploration mode, in which the number of chairs needed for a particular arrangement of tables is displayed; or Guess, in which the user is able to construct an arrangement and then predict the number of chairs. There are two types of tables to choose from and two different table arrangements. Instructions and exploration question are provide.

In this lesson from Illuminations, students explore and discover linear relationships. Linear patterns are identified, extended and described verbally, numerically and algebraically through three investigations. Using manipulatives and the linked applet, "Chairs", learners determine the number of chairs needed when the number of tables is known, and vice versa. Instructional plan, questions for the students, assessment options, extensions and teacher reflections are provided.

An applet for students to use in exploring the area and circumference of a circle in relation to its radius and diameter. When the radius is changed, the other measures automatically change and are shown on a board. Most importantly, the ratio between any pair of these measures can be shown.

This place value and problem solving lesson focuses on forming 3-digit address numbers to meet specific requirement. The lesson provides an opportunity for learners to use the problem-solving strategies of looking for patterns and establishing an organized list. Students also learn that careful reading of information and understanding of mathematical language are important to finding appropriate solutions.

This unit of four lessons highlights different aspects of students’ understanding and use of patterns as they analyze relationships and make predictions, as discussed in the Algebra Standard. In this cluster of activities, students use two interactive math applets (both catalogued separately) to learn about repeating and growing patterns. In the first part, students explore a two-square pattern unit and in the second part, students investigate repeating patterns with pattern units of three, four, and five squares. In Part 3, students analyze repeating patterns of colored cubes and lastly in Part 4, students create growing patterns of colored cubes and compare them to repeating patterns.

This lesson unit is intended to help you assess whether students recognize relationships of direct proportion and how well they solve problems that involve proportional reasoning. In particular, it is intended to help you identify those students who: use inappropriate additive strategies in scaling problems, which have a multiplicative structure; rely on piecemeal and inefficient strategies such as doubling, halving, and decomposition, and have not developed a single multiplier strategy for solving proportionality problems; and see multiplication as making numbers bigger, and division as making numbers smaller.

An online, interactive, multimedia math investigation. The Factor Game engages students in a friendly contest in which winning strategies involve distinguishing between numbers with many factors and numbers with few factors. Students are then guided through an analysis of game strategies and introduced to the definitions of prime and composite numbers.

Using this tool, students build these classic fractals: the Koch snowflake, a fractal tree, a reduced square, and the Sierpinksi triangle. As these shapes grow and change using an iterative process, students can observe patterns in the images created and in the table of values as the fractals progress through several stages.

This lesson unit is intended to help teachers assess how well students are able to identify linear and quadratic relationships in a realistic context: the number of tiles of different types that are needed for a range of square tabletops. In particular, this unit aims to identify and help students who have difficulties with: choosing an appropriate, systematic way to collect and organize data; examining the data and looking for patterns; finding invariance and covariance in the numbers of different types of tile; generalizing using numerical, geometrical or algebraic structure; and describing and explaining findings clearly and effectively.

This lesson unit is intended to help you assess how well students working with square numbers are able to: choose an appropriate, systematic way to collect and organize data, examining the data for patterns; describe and explain findings clearly and effectively; generalize using numerical, geometrical, graphical and/or algebraic structure; and explain why certain results are possible/impossible, moving towards a proof.

This tool allows you to learn about various geometric solids and their properties. You can manipulate each solid, seeing it from every angle. You can also color each shape to explore the number of faces, edges, and vertices. With that information, you are challenged to investigate the following question: For any polyhedron, what is the relationship between the number of faces, vertices, and edges?

This google slide show is for use with grade 1 students as a routine to build number sense in the third quarter. Strings of expressions are used to build connections and as a springboard for discussion. Each slide has a target addition strategy, though other strategies are encouraged as well.

In this 25-day Grade 2 module, students expand their skill with and understanding of units by bundling ones, tens, and hundreds up to a thousand with straws. Unlike the length of 10 centimeters in Module 2, these bundles are discrete sets. One unit can be grabbed and counted just like a banana?1 hundred, 2 hundred, 3 hundred, etc. A number in Grade 1 generally consisted of two different units, tens and ones. Now, in Grade 2, a number generally consists of three units: hundreds, tens, and ones. The bundled units are organized by separating them largest to smallest, ordered from left to right. Over the course of the module, instruction moves from physical bundles that show the proportionality of the units to non-proportional place value disks and to numerals on the place value chart.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

This google slide show organizes hundreds charts number puzzles in a sequence by weeks. Puzzles are online and linked to this slide show. Teachers can use these with students to promote number sense, addition, subtraction, and place value.

This google slide show will be used by third grade teachers with their students as a numeracy routine. Students should be given time to notice and wonder about each slide. Students then engage in discourse to find which two statements are mathematically correct and which one is not.

This google slide show organizes place value exercises in a sequence by weeks. Teachers use the slide show with students to promote finding structure and adding and subtracting ones and tens.

This google slide show will be used by fourth grade teachers with their students as a numeracy routine. Students should be given time to notice and wonder about each slide. Students then engage in discourse to discuss the mathematics found in the images.

The activities in this 6-lesson unit use fish-shaped crackers to help students develop their understanding of comparative subtraction by exploring five meanings of subtraction (counting, sets, number line, balance, and inverse of addition). Students investigate properties of subtraction, represent subtraction with objects and pictures, record subtraction with vertical notation and equations, create and solve problems, and carry out missing addend activities. Lessons include questions for student discussion and teacher reflection, extensions, printable student sheets, assessment options, and links to online applets.

In this unit plan, primary learners explore the five models of subtraction (counting, sets, number line, balanced equations, and inverse of addition) using concrete (links), pictorial, and verbal representations to develop an understanding of symbolic notations. Students also investigate fact families, including those where one addend is 0 and where the addends are alike and also learn that the order (commutative) property) does not hold for subtraction. A brief bibliography of related books for children is provided. Instead of using hands on manipulatives and balances, links to Java applets: Pan Balance-Shapes and Pan Balance-Numbers ( both cataloged separately) are included. Instructional plan, questions for the students, assessment options, extensions,and teacher reflections are given for each lesson as well as links to down load all student resources.