This lesson focuses on the observation of properties and the classification of objects to build ideas about variables. Learners compare buttons to identify similarities and differences. In addition, learners are introduced to Venn Diagrams by reading "The Elves and the Shoemaker" and sorting their shoes in a giant diagram.

This unit consists of four lessons in which students explore several meanings and representations of multiplication, including number lines, sets, arrays, and balance beams. They also learn about the commutative property of multiplication, the results of multiplying by 1 and by 0, and the inverse property of multiplication. Students write story problems and create pictographs. The unit includes activity sheets, assessment ideas, links to related applets, reflective questions for students and teachers, extensions and a bibliography of children's literature with a multiplication focus.

In this data analysis activity students investigate data in connection with recyclable materials and develop plans to help the environment. Students collect data about aluminum can usage and graph that data in a line plot. The lesson includes student worksheet and extension suggestions.

In this 5-lesson unit primary students identify attributes of buttons and other objects in their classrooms. Throughout the unit students learn to collect data about objects, display the data (Venn diagrams, pictographs, and bar graphs), and analyze the data to determine what this tells us about buttons and/or other objects. Each of the five lesson plans includes necessary student/class worksheets, questions for students, extension ideas, and assessment ideas. Lessons 2 and 3 reference stories that are an important part of the skill development: "The Button Box" by Margarette Reid and "The Elves and the Shoemaker" story.

In this math activity, learners explore the history of the Stomachion (an ancient tangram-type puzzle), use the pieces to create other figures, learn about symmetry and transformations, and investigate the areas of the pieces. The Stomachion, believed to have been created by Archimedes, consists of 14 pieces cut from a square, which can be rearranged to form other interesting shapes.

This semester students are asked to transform the Hereshoff Museum in Bristol, Rhode Island, through processes of erasure and addition. Hereshoff Manufacturing was recognized as one of the premier builders of America's Cup racing boats between 1890's and 1930's. The studio however, is about more then the program. It is about land, water, and wind and the search for expressing materially and tectonically the relationships between these principle conditions. That is, where the land is primarily about stasis (docking, anchoring and referencing our locus), water's fluidity holds the latent promise of movement and freedom. Movement is activated by wind, allowing for negotiating the relationship between water and land.

Establishes basic attitudes toward architectural organization and its reflection in form. Includes projects where imposed conditions of site, program, and building system emphasize the interrelationship of fundamental elements in the pattern of decision-making that constitutes architectural design. Develops presentations through drawings and models. Intended for entering M.Arch. students. Course Description This studio explores the notion of in-between by engaging several relationships; the relationship between intervention and perception, between representation and notation and between the fixed and the temporal. In the Exactitude in Science, Jorge Luis Borges tells the perverse tale of the one to one scale map, where the desire for precision and power leads to the escalating production of larger and more accurate maps of the territory. For Jean Baudrillard, "The territory no longer precedes the map nor survives it. ĺÉit is the map that precedes the territory... and thus, it would be the territory whose shreds are slowly rotting across the map." The map or the territory, left to ruin-shredding across the 'other', beautifully captures the tension between reality and representation. Mediating between collective desire and territorial surface, maps filter, create, frame, scale, orient, and project. A map has agency. It is not merely representational but operational, the experience and discursive potential of this process lies in the reciprocity between the representation and the real. It is in-between these specific sets of relationships that this studio positions itself.

This two-lesson unit from Illuminations, exposes students to algebra, measurement, and data analysis concepts and the major theme of analyzing change. In the first lesson, students measure the heights of classmates and older students and construct a table of height and age data to compare them. The second lesson's instructional goal is to understand how change in one variable, age, can relate to change in a second variable, height. Instructional plan, questions for the students, assessment options, extensions, and teacher reflections are given.

Novel representations and diverse perspectives can reveal new insights into complex systems, and can support rich understandings of the world. In this activity, students will identify and analyze the choices artists and scientists make when creating representations of living or non-living natural objects. This process will help students recognize the potential and place for their own articulation of how the world works. After drawing from nature, students will reflect on the process of representing information, then compare their drawings with that of a 16th-century artist. Students will consider what is included and what is excluded, and hypothesize about larger contexts and systems.

In this lesson students use a rule of thumb about the weight of babies to practice doubling and halving numbers. They complete an organized table and compare data using vertical and horizontal double bar graphs. The lesson includes a student activity sheet and extension ideas.

In this lesson plan students conduct a survey of ten students, collect data in a tally chart, and then display and analyze the results in a bar graph. In the analysis students must compare numbers, add, and subtract using the data in the bar graph to generate questions as well as answer them. The lesson plan includes a graph template, a link to an interactive graphing tool, extension questions, and a fact family sheet to show the related facts from their graph analysis.

In this math activity, learners are challenged to create aluminum foil boats that will hold plastic bears until the boats sink. The lesson serves as a fun, hands-on way to collect data. Data from two attempts is collected and used to make two class box-and-whisker plots with some surprising results. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

In this 8-lesson unit students use buttons to explore logical and numerical relationships that form the conceptual basis for understanding addition and subtraction operations. Topics include counting, ordinal numbers (and relative position), classification (attributes), relationships between numbers, addition of sets, commutativity of addition, sums to 10, fact families (including subtraction), three models of subtraction ("take away", comparative, missing addend), and bar graphs. Includes student activity sheets and a link to an online graphing applet.

In this 8-lesson unit students use buttons to explore logical and numerical relationships that form the conceptual basis for understanding addition and subtraction operations. Topics include counting, ordinal numbers (and relative position), classification (attributes), relationships between numbers, addition of sets, commutativity of addition, sums to 10, fact families (including subtraction), three models of subtraction ("take away", comparative, missing addend), and bar graphs. Includes student activity sheets and a link to an online graphing applet.

This article provides a brief discussion of the importance of teaching students to analyze data and representations of data as well as two resources that can help teachers implement these strategies into their instruction.

In this Illuminations lesson plan students explore the use of variables as they solve for the weights of objects using information presented in pictures. Learners model situations that involve adding and subtracting whole numbers, using objects, pictures, and symbols. A student activity sheet is available and downloadable (pdf).

This interactive applet introduces students to the topic of combinations, a basic concept in probability. Users create combinations of shirts and pants to determine the total number of possible outfits. They may simply explore by placing the clothes on Bobbie, or make a guess and then test it. The number of shirt and pants choices is customizable. An optional voice provides prompts and feedback.

This Flash tool allows students to make a box plot of their data, using up to four categories of their own choosing, or using one of the data sets provided. The tool will plot all the data together, or break it out by category. Students can set a multiple of the Interquartile Range to be the Extreme Range, and exclude that data from the graph if they wish. Associated lessons (free) and a Mathematics Assessment Sampler (for purchase) are linked at the right side of the page.

This lesson helps students develop spatial visualization skills and geometric understanding by exploring the different nets that can be folded into a cube. The lesson is placed in the context of a young woman who is trying to build a jewelry box. The lesson provides an activity sheet, a link to a helpful applet (Cube Nets, cataloged separately), questions for students and teachers, and ideas for assessment and extensions.

Using the story "The Celebrated Jumping Frog of Calaveras County" by Mark Twain, learners simulate a jumping-frog contest and determine the distances "jumped." Learners record the distance of individual jumps in centimeters and determine the total distance jumped (the sum of the three separate jumps) and the official distance (the straight-line distance from the starting line to the end of the frog's third jump). Learners compare the range and median of the total distances with those of the official distances of the group.