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Algebra

Fish Food, More or Less

Pre-K-2

Students are introduced to the concepts of greater than, less than and equal to by observing quantities and making comparisons. Using various instructional materials such as modeling clay, buttons, beans, and cotton balls, students create amounts to compare using the open-mouthed fish. Depending which fish is chosen, the fish cut-out (with its mouth open) represents either greater than or less than. For equivalent amounts, a clam cut-out represents equal to.

This introductory lesson can be assessed through visual observation and verbal questioning. A group size of 3 – 6 students per group is optimal.

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Algebra

From Fish Food to Pictures to Symbols

Pre-K-2
Students build upon their understanding of greater than, less than, and equal to by observing quantities and making comparisons using various instructional materials. The fish cut-out, with its mouth open, represents the greater than or less than symbol; the clam cut-out represents the equal to symbol. Using fish lips as a transition point, students will apply their understanding of greater, less, and equal to the standard symbols (>, <, =) as you introduce symbolic notation at a developmentally appropriate level.
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Data Analysis and Probability

Alike and Different

Pre-K-2
This lesson focuses on the observation of properties and the classification of objects to build ideas about variables. Students compare objects to identify similarities and differences. In addition, students are introduced to Venn Diagrams.
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Data Analysis and Probability

Naming Rows and Columns

Pre-K-2
In this lesson, the teacher models how to organize data and use the vocabulary associated with collecting, organizing, and displaying data. Students learn the difference between rows and columns, how to label and select a title for graphs, and what comparative terms to use to describe relationships between and among the various sets of buttons.
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Data Analysis and Probability

Show and Tell

Pre-K-2
This lesson allows students to describe their graphs using appropriate vocabulary and to develop skills in posing and responding to questions about their graphs. Students also demonstrate an understanding of how to organize and interpret data. In addition, this lesson helps students move from the concrete through pictorial to abstract representations of displays of data, namely a graph.
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Measurement

My Pet

Pre-K-2
In this lesson, students develop and use spatial relationships and spatial memory by creating a map of a pet. The students use visual and spatial skills, measure with nonstandard units, and describe "trips" around their pet using directional and positional words.
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Measurement

Puzzling Relationships

Pre-K-2

Puzzles provide excellent opportunities for students to apply spatial relationships in an entertaining and meaningful way. In the first part of this lesson, the students use concrete materials to develop the skills needed to work with interactive tangram puzzles in the second part of the lesson. The students also further develop their understanding of spatial relationships and develop problem-solving skills.

Once students complete puzzles using concrete materials, introducing them to virtual puzzles enables them to experience turns, rotations, slides, and spatial relationships in a powerful way. These transformations are more apparent in a virtual environment than when using concrete tools.

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Measurement

Measuring Me

Pre-K-2
Students use yarn to measure lengths such as arm span and height. This gives the students practice measuring with nonstandard units. Pairs of students also compare their height and arm spans. They practice problem-solving and reasoning skills by discussing why there are similarities and differences between the lengths of yarn that represent arm spans and height.
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Data Analysis and Probability

Why Is California So Important?

6-8
In this lesson, students learn about the mechanics of the Electoral College and use data on population and electoral votes for each state. Students calculate the percentage of the Electoral College vote allocated to each state, and use mathematics to reflect on the differences. Several questions are provided to strengthen understanding of measures of central tendency and fluency with decimals and percents.
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Number and Operations

How Could That Happen?

6-8
This problem-solving lesson challenges students to generate election results using number sense and other mathematical skills. Students are also given the opportunity to explore the mathematical questions in a politically challenging context. Calculations can be made using online or desktop tools or using the data gathered on the Lesson 1 activity sheet, Why California?  Additional resources are introduced to extend the primary activity.