# Living Math Through History - Samples and Details

Below are samples of each level of lesson plans. Some information will appear on all levels. Differences are in the reading materials, discussion activities, and mathematical activities which are tailored to each age group.

Some materials will overlap levels if they may be used by students who are borderline. This is explained in the Parent Introduction letter.

**Primary Level Lesson Plan Sample**

(approximately lower elementary level)

**Intermediate Level Lesson Plan Sample**

(approximately upper elementary to middle school)

**Advanced and High School Levels Sample Lesson Plan**

(Dual level upper middle school to high school/adult)

*Parent Introduction Letters:** *** Primary**,

**Intermediate**,

**Advanced / High School**

* Additional Lesson Plan Details: *These lessons plans are are intended to provide a multi-level structure for home educating or afterschooling families to study math through history and related math topics in context. Reading guides, suggested activities and online support are provided for Primary, Intermediate, Advanced and High School Levels (see Samples and book lists /comments related to reading levels).

There is no need to keep up with a group schedule as lessons are self paced. The lessons feature a biography of one or more mathematicians, with reading assignments, resources, suggested links and activities tying in with the concepts and history surrounding the individual studied. Plans include identification of the geographical origins of the person studied, historical events of the time, contemporaries, etc.

The course does not have a solely Western European math history focus; Eastern contributions and contributions by women are studied. The levels lock-step the math history personages, but the reading depth and activities will vary according to level. This is beneficial to families with multiple aged siblings for discussion, activities, reading aloud, etc. Activities are offered as they relate to the work of people studied, including the following topics: Probability, finance, geometry, number patterns and sequences, logic, and algebra, word problems, making your own problems. Yes, you can introduce and play with these topics even with early elementary children if the goal is not mastery, but exposure and familiarity.

Access to one set of plans provides access to all activities, as "grade levels" do not apply to many activities. Lessons give attention to the effect of language on math through exploring, comparing the differences in mathematical word meanings vs. other life applications. Suggested activities to discover areas where language causes mathematical confusion, such as “reducing” fractions, double negatives, etc. Activites will be suggested to explore mathematical poetry and literature, the relationship between math and music, math in nature and life.

Parental participation for the primary and intermediate levels will be necessary to get the most out of this, advanced (approximately 7th grade and up) will have clear enough instructions that parental participation would be related to assistance as needed and follow through. But some older students will gain more if a parent studies and discusses the material with them.

* Primary Level (approximately 1st-3rd Grades) *: Lessons for this class will consist primarily of read alouds, map / geography skills and suggested games related to the math history topics. I suggest vocabulary and other language oriented math activities. Much of the math activities in this level come from picture books used in the course. Note re kindergarten:

You are encouraged to use the booklists and wait on formal lessons for kindergarten to 1st grade. If you feel your child is ready or has an interest in activities, however, you may want to give the plan material a try. Some families use the materials with this age and spread it out over a long period of time.

* Intermediate Level (approximately 4th - 7th Grades) *This group will also cover the math history, but with more advanced reading, discussion and activities. Similarly to the primary level, there will be suggested games and activities, but assume multiplication is conceptually understood. Lessons include read alone and/or readaloud (some read alouds will track with the primary level), map / geography skills and weekly suggested games/activities related to the math history topics. Vocabulary and language oriented math activities will be suggested, as well as internet site based activities.

* Advanced Level (approx 8th - 9th) *Similar in structure to the intermediate, but with more reading at higher levels. Math levels vary, so access to all activities allows you to use activities that track with the math capability of the child.

* High School (approx. 10th and up) *The math history outline for this group will be the same, but the reading will be based more on selected adult level materials including reading excerpts from mathematics and science classes such as Euclid's Elements, Galileo's and Kepler's writings, Newton's Principia, etc. If all the challenging reading is used, this is a serious course of study in a college preparatory model. Basic elementary math skills are assumed, There is exposure to algebra, geometry, calculus, logic, etc. in exploratory context without requirement for mastery.

**Answer: **Materials needed are listed at the **Book Lists** and in the plans. Some materials I recommend you purchase as they are used throughout the historical cycle, or through quite a few lessons. Others can be obtained via library resources. Many families use inter-library loan services.

I strongly suggest you review the plans before purchasing to see what you can borrow or might already have or can skip, since I suggest some optional resources in the plans that aren't on the main list. The plans are available upon sign up.

Bookcloseouts used to be an excellent source of discount math readers, but in recent years has discontinued carrying many of the best readers. Amazon frequently has math readers on sale, however, on a 4-for-3 basis.

**How do I use the plans with several levels at once?**

**Answer: **You can bring a wide age range of kids together for readaloud times from the "spine" readers (readers used throughout the plans). Older kids will be able to read their assignments on their own, and it will be up to your discretion and your family dynamics as to how much to integrate them into the younger children's time.

Ages 12 and up are often able to be more self-directing of their assignments, and you would be in the role of discussing and involving them in activities, rather than "teaching" or instructing them. I do, however, spend a great deal of time in discussion even with my older children, as this seems to be where the greatest benefit is derived.

I personally find that when my family is studying the same things, we tend to talk about them at the dinner table, rent videos that have to do with the content we're studying, etc. How much time you put into it will vary based on how much reading aloud you have to do, vs. what the kids can read on their own, and whether you are reading along with older kids. I read the Mathematicians Are People, Too books to my oldest even up to age 11 along with an 8 y/old and 6 y/old sibling. The Joy of Mathematics has activities that are adaptable to all ages.

My children have taken art history classes for a couple years from a teacher that has the older and younger classes track topics with each other, and one thing I have done is have the older children help the younger with some of the activity work. This reinforces things the older children are learning and frees me up as well. Only you know whether the dynamics in your family will permit this.

Other ideas may be gleaned from the parent support list.

**Can I buy books from Living Math?**

**Answer:** Selling books takes too much time away from writing and family. One reason the book list pages are linked to Amazon is so that you can comparison shop, however. Sales through those links does provide a small amount of credit to benefit this site.

**Do I use math curriculum with the plans?**

**Answer:** Ah, the big question. If you are good at learning how to weave math into daily life and use the suggested activities and links, have access to the books, there is a great deal of math in the lesson plans. You may or may not want to add curriculum to the Primary and Intermediate levels. Ultimately my goal is directed to bringing in more math content that can be tied to Californiastandards if a parent wants the assurance of knowing all the bases are covered over time, but it would not be a traditional path.

Our family over the years has blended living math with curriculum resources, but living math has been the foundation, not the other way around. We have added curriculum in and used it as a source of problems or presentations of ideas we study in living books. But we we have also taken an entire year off of curriculum at a time if math reading and activities was generating a lot of interest and productive learning. We also use video resources and any other math materials we enjoy. This can be referred to as an "eclectic approach" and it works for us.

Other families have successfully used the course as a break from traditional curriculum. One family shared that they work three weeks on curriculum and then take a one week break to do Living Math. Others share that they do traditional math three days a week and use Mondays and Fridays as living math and game days. Some do the reading as their bedtime read alouds and do activities one day a week while following a math curriculum, or use Living Math plans for history. Some use Living Math for more extended breaks from curriculum when their children are burned out from traditional math work.

For the advanced levels, while there is a lot to be learned through this type of study, a text or class will be necessary to learn modern algebra, geometry, pre-calculus and/or calculus. Families using advanced level materials are using a wide variety of materials, and included in the plans are suggestions of materials that tend to be compatible with this approach. The LivingMathForum list is an excellent place to ask questions about various advanced learning materials that might be appropriate.