Tag Archives: numeracy

A Lesson Plan on the Admission of the First 13 of the United States from The Order of Things

Here is something new at Mark’s Text Terminal: a reading and analysis lesson plan derived from the text of Barbara Ann Kipfer’s book The Order of ThingsI’ll be writing up a summary of this work and its purpose on the “About Posts & Texts” page, which you can click through to just above the banner photograph. I am still thinking through how to describe the object of these lessons (I have 30 of them outlined at this point), but I can say this much: these worksheets are an attempt to provide students practice, as a road to developing their own understanding of what former U.S. Secretary of Labor Robert Reich called the work of “symbolic analysts.”

This first lesson plan is on the admission of the first 13 of the United States. The worksheet for this lesson calls upon students to read and analyze both language and numbers (two sets of symbols, in other words) in order to answer a series of relatively simple comprehension questions. There is a lot of room to alter this material to you and your students’ needs; as always, these documents are in Microsoft Word, so they are easily manipulable.

More of these are forthcoming, as is a more extensive explanation of them and rationale for their use, as above, on the “About Posts & Texts” page.

If you find typos in these documents, I would appreciate a notification. And, as always, if you find this material useful in your practice, I would be grateful to hear what you think of it. I seek your peer review.

A Lesson Plan on Understanding and Differentiating Historical Dates

Here is a lesson plan on understanding and differentiating historical dates which I have actually previously posted on Mark’s Text Terminal. While this is a social studies lesson on understanding how we use numbers to count and describe historical time, it has an ulterior literacy motive in that it seeks to help students, particularly the many English language learners I have served over the years.

We use two types of numbers when we talk about historical dates, ordinal and cardinal. Ordinal numbers are adjectives that, as their name indicates, place things in order. So, when we use terms like fourteenth century, fifteenth century, and so on, we are using ordinal numbers. Similarly, when we say, respectively, the 1300s, the 1400s, and so on, we are using cardinal numbers, which are nouns and which we use to count things. These two types of numbers are different in English just as they are different in other languages. Because I didn’t initially understand the difference between these kinds of numbers, I struggled to understand the numbering system in Russian when I studied that language.

For that reason, I wrote this context clues worksheet on the adjective ordinal and this on the noun phrase cardinal number. These worksheets aim to help students understand the difference between these two types of numbers and their use in English prose. This is knowledge that transfers across the curriculum–to foreign languages, English language arts, mathematics itself, and, yes, social studies.

Finally, here is the combined learning support and worksheet that is the gravamen of this lesson.

If you find typos in these documents, I would appreciate a notification. And, as always, if you find this material useful in your practice, I would be grateful to hear what you think of it. I seek your peer review.

360 Degrees

“The circle is divided into 360 degrees, which is an attempt to create a perfect universe out of our slightly wonky one. For 360 can be neatly divided by 4 to make 90-day seasons, or by 12 to make perfect months of 30 days, or by 18 to make 20-day units. This perfect ordering of the world—the sexagesimal system—was codified by the Babylonians and still orders the world of geometry and time-keeping with 60 seconds in a minute and sixty minutes in an hour.

Of course, the reality of our world was never quite as neat as those Babylonian mathematicians aspired to be, for a lunar month is actually 29 days 12 hours, and 44 minutes, not a neat 30, and a solar year (the time in which it takes the earth to orbit the sun) is actually 365 days, five hours, and 48 minutes, not a neat 360. So, in the old days, we made an odd thirteenth month of five days, before opting to spread them around to make some months 30 days long, some 31. And every fourth year we need our years to be 366 days long, in order to use up an extra day acquired by four additional units of five hours and 48 minutes.

Nonetheless, the perfection of 360 has always been aspired to, with ancient stone circles formed of 360 stones and altars formed from 360 cut stones.”

Excerpted from: Rogerson, Barnaby. Rogerson’s Book of Numbers: The Culture of Numbers–from 1,001 Nights to the Seven Wonders of the World. New York: Picador, 2013.

A Lesson Plan on the Timelines of World History

I was all but certain that I had previously posted this lesson plan on the timeline of global history, but I can’t find it anywhere on Mark’s Text Terminal. So, here is a context clues worksheet on the noun chronology with which I open this lesson. Here is the reading, which is really a list of significant dates in world history; here also are the questions to answer in worksheet form. Finally, here are is the teacher’s copy of the worksheet, i.e. the answers.

If you find typos in these documents, I would appreciate a notification. And, as always, if you find this material useful in your practice, I would be grateful to hear what you think of it. I seek your peer review.

The 8 Gregorian Church Modes

“Dorian * Hypodorian * Phrygian * Hypophrygian * Lydian * Hypolydian * Mixolydian * Hypomixolydian

The exact origins of this eightfold organization of modes that completely dominated the church music of medieval Christendom remains contentious. Most authorities accept that the Carolingian court borrowed them from ninth-century Byzantine liturgies, which themselves arose out of the ancient priestly chants of the Near East.

Just as in ancient Greece, generation after generation of writers sought to define the effects of their emotions. Dorian was considered to be serious and to tame the passions; Hypodorian tended towards the mournful and tearful; Phrygian incited passion and led towards mystical revelry; Hypophrygian was the mode of tender harmony that tempered anger; Lydian was the music of cheerful happiness; Hypolydian was the tone of devout and emotional piety; Mixolydian united pleasure and sadness; and Hypomixolydian aspired to a sense of perfection and secure, contented knowledge.”

Excerpted from: Rogerson, Barnaby. Rogerson’s Book of Numbers: The Culture of Numbers–from 1,001 Nights to the Seven Wonders of the World. New York: Picador, 2013.

8 Long Division Worksheets with Their Answer Keys

I am not a math teacher. Nonetheless, I was in fact tasked with teaching math this year. To that end, I wrote these eight long division worksheets and their respective answer keys. If these work for you, here are three more in another post, and seven more in yet another post. I wrote these as I needed them, I guess.

If you find typos in these documents, I would appreciate a notification. And, as always, if you find this material useful in your practice, I would be grateful to hear what you think of it. I seek your peer review.

7 Ancient Visible Planets

“Sun * Moon * Venus * Mercury * Mars * Jupiter * Saturn

Our sky-watching, hunter-gathering ancestors had 7 marked out as a number of enormous importance for tens of thousands of years. For this is the number of the visible planets—‘the five wanderers,’ plus the sun and the moon.

This respect for the 7 became ever more ingrained as the first agricultural civilizations allowed for accurate fixed observations from the calendar-keeping priests, whose temples throughout the ancient Middle East were all equipped with star-watching terraces above their cult chambers. It is an intriguing element within the cult of the 7 that the planets are not all visible at once: Mercury and most especially Venus (whose horns are occasionally visible) are the morning and evening stars. Bright Jupiter, luminous Saturn, and the more elusive red Mars belong to the full night. So we have always known that we have been watched, influenced, and enclosed by these 7 who right from the dawn of our consciousness have intriguingly different characteristics and hours of dominance and passageways through the heavens.

Although most of mankind probably now accepts that the earth is a planet which circles around the sun, and the moon is a planet of the earth, the mystery of our 7 encircling heavens still haunts our imagination. But this once immutable number of 7 keeps changing. First we knocked the seven down to five (as the sun and moon were taken off the list), then, in relatively modern times, it grew to nine. Uranus was discovered in 1781, followed by Neptune in 1846, then Pluto in 1930 (though this was later demoted to a dwarf planet to bring us back down to eight planets). So, currently, we have eight planets and five dwarf planets (Ceres, Pluto, Haumea, Makemake, and Eris), as well as five named moons orbiting around Pluto.”

Excerpted from: Rogerson, Barnaby. Rogerson’s Book of Numbers: The Culture of Numbers–from 1,001 Nights to the Seven Wonders of the World. New York: Picador, 2013.

Seven Long Division Worksheets with Their Answer Keys

When I was tasked with teaching math this year, I struggled to get up to speed. What I know about teaching math comes from the pages of The American Educator, the American Federation of Teachers’ first rate quarterly of educational research and practice.

Working from what I read in that journal over the years, I proceeded to write these seven worksheets on long division. You will notice that I wrote these to help students recognize patterns and similarities in numbers, which is one of the things students must be able to do to move forward in the domain. Here are the answer keys for those documents. I have another set of eight of these still to post. Whatever utility these have, they can, like just about everything at Mark’s Text Terminal, be adapted to your needs and circumstances: they are in Microsoft Word.

If you find typos in these documents, I would appreciate a notification. And, as always, if you find this material useful in your practice, I would be grateful to hear what you think of it. I seek your peer review. Math teachers, I would be especially interested in hearing from you, particularly in reply to this questions: do these look appropriate for meeting the needs of struggling learners?

Word Root Exercise: Trop/o, -Tropy

Here is a worksheet on the Greek word roots trop/o and -tropy. This is a complicated pair: they mean turning, changing, figure of speech, and responding to a stimulus. A lot of the words in English that grow from this root are abstract and science related–one of them, of course, is trope, which literally means “a word or expression used in a figurative sense: FIGURE OF SPEECH,” and has happily turned up in the American vernacular. But you can also find in a word from physics, entropy.

If you find typos in this document, I would appreciate a notification. And, as always, if you find this material useful in your practice, I would be grateful to hear what you think of it. I seek your peer review.

Kurt Godel

Here is a reading on Kurt Godel along with its attendant vocabulary building and comprehension worksheet. There is room in the document–and the latitude, as, like most other things on Mark’s Text Terminal, these are Word documents that can be edited for your students’ needs–to deal with some of the abstractions Godel’s work deals with.

If you find typos in these documents, I would appreciate a notification. And, as always, if you find this material useful in your practice, I would be grateful to hear what you think of it. I seek your peer review.