## Discovering CCSS Practice Standard 7

The resources in this collection present students with problems, lessons, and activities in which they must look for and make use of structure in order to determine the answer and/or develop the mathematical concept (CCSS Practice Standard 7). Students learn to identify the structure of patterns, data displays, numerical quantities, operations, and geometric figures. Additional resources for educators can be found in a companion Professional Development collection, "CCSS Practice Standard 7."

## Collection Discussion

No discussion topics are created for this Collection.

This series of activities can be used to introduce number sequences and patterns and to reinforce parity (even and odd numbers) and its application in addition. The resources are intended for use on an interactive whiteboard but may also be used individually or in small groups. They can be accessed online or downloaded (zip) to a local computer. The pack includes teacher notes, background information on the content, and a student worksheet.

This set of two interactive challenges from the Annenberg Teachers' Lab helps learners investigate patterns in form and in syntax in language. In "Limerick Factory" users discover the limerick rhyme scheme (A-A-B-B-A) by making limericks online with pull down menus. In "Syntax Store" learners work with parts of speech and the way words and phrases are put together to make a sentence. Background discussion, a rationale, grade-level information, connections to standards, and solvers' comments are included for each activity.

This Java applet presents a composite number, and prompts you to factor it -- one step at a time. Enter one factor, prime or another composite; the applet calculates the remaining factor, and branches two boxes below any composite factor so that you may proceed factoring until you obtain the full factorization into primes, which the applet colors in green. Click the "Repeat problem" button to see that different factor trees for a given number still result in the same prime factorization.

This puzzle, played with cards on a board (downloadable file), provides an interesting context in which students can apply their knowledge of number properties. Students attempt to arrange 25 numbers and 10 property headings into a 5 by 5 grid so that each number satisfies two conditions. Properties addressed include primes, square and triangular numbers, specific sets of multiples and factors, and parity. It can be worked individually or in small groups cooperatively. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and links to an article, "Using Games in the Classroom" (catalogued separately).

In this activity students are asked to relate the numbers 1- 20 to rectangular shapes. Learners use unit squares or cubes to sort numbers by their 'shapes,' either squares, rectangles or sticks (rectangles of unit width). Ideas for implementation, extension and support are included.

This lesson and interactive applet lets students explore geometric relationships and make and test conjectures. The main task centers on identifying what distinguishes a rectangle from a more general parallelogram. Students manipulate both figures and look for comparisons. Suggestions for implementation and supplemental tasks are provided.

This activity asks students to visualize shapes, paying close attention to the definitions of special polygons. Learners are given a sheet of isometric grid paper and asked to find and sketch 12 specific shapes. Ideas for implementation, extension and support are included along with printable grids and shape definitions.

This lesson plan provides a context for reading trends in line graphs. The lesson plan incorporates an investigation in conjunction with a Cyberchase video to get students to discover and discuss the best way to representa set of data. The lesson plan includes two short video clips, two worksheets, and two assessments options.

In this number sorting activity students must use a Carroll Diagram to determine which two categories each number fits into. This activity can be completed in pairs or groups on printable versions or it can be completed as a whole class using the interactive white board (IWB). Included with this resource are printable versions of the Carroll Diagrams, guiding questions, extension and support suggestions, and a link to more challenging "More Carroll Diagrams".

This 37-page pdf provides background information and teaching activities for developing young children's number sense. The document includes instructions and printable materials for using dot cards, five frames, and ten frames.

Students can use this interactive Flash applet to practice subitizing and counting groups of objects, to develop awareness of our base-10 number system, and to learn basic addition facts. In the four included games students construct groups of 10 objects, add groups of objects within 20, and identify and record numbers within 20. Auditory prompts support students with limited reading ability.

Students can use this interactive Flash applet to practice subitizing and counting groups of objects, to understand the importance of 5 in our base-10 number system, and to learn basic addition facts. In the four included games students construct groups of 5 objects, add groups of objects within 10, and identify and record numbers within 10. Auditory prompts support students with limited reading ability.

Teachers can use this interactive tool to help students build a conceptual understanding of fractions by creating artwork on a grid, where each color represents a fraction. Students learn how fractions are related to each other and that their value is determined by the value of the unit. This page includes a video demonstration of the tool and sample lessons from the Conceptua curriculum. Free registration is required to use the tool. A paid subscription is necessary to access full curriculum and allow full student use.

This problem is designed to help young learners use the symbols plus, minus, multiplied by, divided by and equals to, meaningfully, in ten number statements. Students must drag two operational symbols to empty boxes to make a true statement. This problem also helps learners understand inverse operations and to look for alternate solutions. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support, printable worksheet.

This lesson helps students develop conceptual understanding of 2-digit multiplication. Students decompose 2-digit numbers, model area representations using the distributive property and partial product arrays, and carry out paper-and-pencil calculations from the arrays. Included are student activity sheets, a link to a supporting online applet, and extension suggestions.

This web unit leads students to discover how to construct Pascal's triangle. Other activities include coloring odd (or even) numbers or the coloring of multiples of numbers. Student worksheets displaying Pascal's Triangles of various sizes, empty or filled, are included. The Teacher Reference graphically reveals number patterns found within Pascal's Triangle including natural numbers,triangular numbers, Fibonacci numbers, powers of 2, and many others.

In this application students determine the location of Grampy when given the denominator of the fraction and his general location behind the hedge (number line). Students input the expected numerator for Grampy's location. Directions are included beneath the activity. This resource is part of Visual Fractions which is cataloged separately.