Day six is the perfect day for secondary students to investigate perfect numbers as 6 is the first perfect number. Perfect numbers are whole numbers such that when you add up all of the factors of the number that are less than the number itself, you get the number. This activity is also good for students with dyslexia and language-based learning deficiencies.

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Understanding multiple representations are one way that students show evidence of fluency with a topic. See how using multiple representations while investigating place value can help students deepen their understandings of this foundational topic. Several pieces of children’s literature will be shared as well.

The number five is the next number for the 12 Days of Christmas. Secondary students can choose from a variety of investigations all relating to circles. The most basic task is the classic circle in a square. I have also included a figure with various points still shown that some students may find beneficial as they are working. For an alternate task a circle has been circumscribed as well as inscribed in the square. For an interesting twist, have students study the figure and generate a list of questions that might be of interest based upon the figure. Again a figure with selected points has also been provided. Other tasks can be given to students based upon any of the other figures that have been included as well as researching Descartes' Circle Theorem.

Today students of all ages will play will working with one of my favorite mathematical topics of all time: Pascal’s Triangle! Beginning and young mathematicians will be introduced to the triangle. Students can spend a lot of time “tinkering with” the triangle as they discover more and more patterns. The following is an adaptation of one of the chapters in the Primary Activity Packet for Rooster’s Off to See the World, eBook by Tammy L Jones that can be found here on TES USA or TES UK. This activity is great with students with dyslexia and language-based learning deficiencies. Please leave a review.

Today students of all ages will play will working with one of my favorite mathematical topics of all time: Pascal’s Triangle! Intermediate and middle school students, if they are not familiar with the triangle, can investigate the basic structure of the triangle using the 12 Days of Christmas as the backdrop. See the K3 activity for some questions/patterns that are appropriate for introductory work with the triangle. Blank triangles and work mats are also provided in the K3 activity pack. Be sure to have students first investigate the triangle and discover the basic pattern of creating the triangle before they move forward. This activity is also great for students with dyslexia and language-based learning deficiencies. Please leave a review.

Eleven is the first “teen” number beginning mathematicians encounter. Eleven is also the first 2-digit prime number. Older mathematicians will study other 2-digit prime numbers using the Sieve of Eratosthenes. We'd really like to hear about your experience with our resources. Just give it a star rating then tell us what you think, simple as that!

Eleven is the first “teen” number beginning mathematicians encounter. Today’s activity employs children’s literature and manipulatives. If possible, use the children’s book 12 Ways to Get to 11 by Eve Merriam. Have Cuisenaire rods, unifix cubes, or other manipulatives on hand for students as needed. Based upon the individual needs of your children show them the title and allow them to work in pairs to see how many of the 12 ways they can discover to make 11. Alternatively, as you read the story allow the children time to model the various compositions of 11 that are shown in the story. Encourage children to use various representations for their models – drawings, words, equations, sketches of their manipulative models, etc. This activity is good for students with dyslexia and language-based learning deficiencies. We'd really like to hear about your experience with our resources. Just give it a star rating then tell us what you think, simple as that!

For day six younger mathematicians will be looking at multiple representations for the number 6. Facilitation notes and suggestions for differentiation are provided. This activity is also good for students with dyslexia and language-based learning deficiencies.

This is a list of hyperlinked interactives provided by NCTM Illuminations.

This is a list of hyperlinked interactives provided by NCTM Illuminations.

Five golden rings inspire tasks that involve writing about circles to working with circles. There are several options depending upon the needs of your students. • The first task is writing about what makes zero special. Zero is framed in a circle as a visual prompt for students to think about a circle not having any sides. • The second task has students going on a “Circle Hunt”. • The third task has students using circle counters to decorate a Christmas tree (work mat provided) while composing and decomposing numbers. Facilitation notes for the task are provided .

One of the gold standard resources for mathematics is NCTM’s Navigating Through…series. Each grade band series includes books for Navigating through - Algebra, Data Analysis and Probability, Discrete, Geometry, Measurement, Number and Operations, and Problem Solving and Reasoning. The investigations in the series provide opportunities for students to reason, conjecture, and communicate about mathematics. Having used the series for years, I saw a need to quickly be able to locate potential lessons and activities. This compilation includes the lesson title and the goals. On a PC use “Ctrl F” and on a Mac use “Command F” to search for lessons and activities by key word.

One of the gold standard resources for mathematics is NCTM’s Navigating Through…series. Each grade band series includes books for Navigating through - Algebra, Data Analysis and Probability, Discrete, Geometry, Measurement, Number and Operations, and Problem Solving and Reasoning. For Middle School and High School there is also a Connections book in the series. The investigations in the series provide opportunities for students to reason, conjecture, and communicate about mathematics. Having used the series for years, I saw a need to quickly be able to locate potential lessons and activities. This compilation includes the lesson title and the goals. On a PC use “Ctrl F” and on a Mac use “Command F” to search for lessons and activities by key word.

One of the gold standard resources for mathematics is NCTM’s Navigating Through…series. Each grade band series includes books for Navigating through - Algebra, Data Analysis and Probability, Discrete, Geometry, Measurement, Number and Operations, and Problem Solving and Reasoning. The investigations in the series provide opportunities for students to reason, conjecture, and communicate about mathematics. Having used the series for years, I saw a need to quickly be able to locate potential lessons and activities. This compilation includes the lesson title and the goals. On a PC use “Ctrl F” and on a Mac use “Command F” to search for lessons and activities by keyword.

Day five has students writing about circles. The “Writing About…” activity has proved very popular in all disciplines as it supports making writing about mathematics accessible to many students who might otherwise be challenged. The facilitation notes are provided below. As an alternate task (or additional) there is a discrepant activity. They then write about the investigation and the outcomes as well as their prediction.

Five golden rings inspire tasks that involve writing about circles to working with circles. There are several options depending upon the needs of your students. • The first task is writing about what makes zero special. Zero is framed in a circle as a visual prompt for students to think about a circle not having any sides. • The second task has students going on a “Circle Hunt”. • The third task has students using circle counters to decorate a Christmas tree (work mat provided) while composing and decomposing numbers. Facilitation notes for the task are provided.

A look at situations that are meaningful to students and that use inequalities. A look at the two concepts on which inequalities are based will be shared as well as a variety of applications using inequalities.

This is a list of hyperlinked interactives provided by NCTM Illuminations.

A variety of ideas and resources will be shared that can be used to support retention of material as well as enrichment. The resources and activities engage students during the summer break so they are ready to hit the ground running as they return to school in the fall.