Language Decisions in Illustrative Mathematics 6-8 Math

A wide-ranging team worked together to develop the Illustrative Mathematics Grades 6-8 Math curriculum. Many of the authors were and are experienced teachers of Grades 6-8, while others are experienced high school teachers.

My own experience is as a high school teacher, then a high school curriculum writer. One of the ways the team’s experiences led to a higher-quality product was the discussion around language and terms used throughout.

I remember one discussion vividly in building the Grade 6, Unit 2 materials introducing ratios and proportional reasoning. The lead writer was discussing the different representations that would appear in the unit.

Lead writer: “We’ll do diagrams, then double number lines, then ratio tables…”

Me: “What’s a ratio table?”

Lead writer: “What do you mean, what’s a ratio table? Have you never heard of a ratio table?”

Me: “No, never.”

Lead writer: “It’s a table of equivalent ratios, like 1 3 then 2 6 then 5 15 then 10 30.”

Me: “Oh. I get it now. Why don’t we just call these things tables of equivalent ratios?”

It’s subtle, but there are good reasons for doing this.

  • First, the term “ratio table” disappears — by that, I mean it’s used in a particular grade or grades and then not used in later grades’ work. When this happens with vocabulary, it suggests the vocabulary is not really useful and could be removed.
  • Second, the term “ratio table” hides its meaning — that all the rows in the table consist of equivalent ratios. Any table is a ratio table! Students have just learned the phrase “equivalent ratio” within the same unit, so burying that phrase and concept could lead to substantial difficulties.
  • Third, kids are just coming to understand what a “table” is to begin with. By specializing to “ratio table”, kids don’t have a clear sense of what would or wouldn’t be true of other tables.
  • Last, reducing the overall vocabulary load keeps the focus on key concepts, and is especially helpful for students who are below grade level or are English language learners.

So, the lesson that introduces this concept refers to a “table”; the next lesson calls them  “tables of equivalent ratios“.

You’ll find the same level of care throughout the curriculum, and it leads to a relatively clean and short glossary for each grade.

The same thing is also happening behind the scenes: as a team of writers, we try to speak with the same voice and make the same decisions. For example, here are some decisions the team made:

  • Ratio notation. Never 2 cm : 3 cm. Instead, “the ratio of length to width is 2 : 3.” To indicate scale of a map say, “We are using a scale of 1 in to 10 ft” or “On this map 1 in represents 10 ft.” (Because “in to” looks like “into,” for the sake of readability it may be helpful to spell out units, e.g., “The scale is 1 inch to 10 feet.”)
  • No use of the term “improper fraction.”
  • Satisfy and satisfied, as in “satisfy an equation,” are not used in student-facing text. Use instead: “make the equation true.”

These decisions were compiled into multiple style documents, including a 54-page overall writer’s style guide. Here’s a piece of its table of contents:Screen Shot 2018-01-09 at 4.30.24 PM

And here’s the table on “Plain Language”, ways to reduce the reading load and the Fleisch-Kincaid grade level of the work:

Avoid Try
accomplish carry out, do
accurate correct, exact, right
adjacent to next to
advise recommend, tell, suggest
assist, assistance help
attempt try
concerning about, on
comprise form, make up, include
consequently so
consolidate combine, join,
constitutes Is, forms, makes up
contains has
determine decide, figure, find
due to the fact that because, since
eliminate cut, drop, end
employ use
ensure make sure
enumerate count
establish set up, prove, show
facilitate ease, help
failed to didn’t
for a period of for
frequently often
however but
identical same
identify find, name, show
in addition also, besides, too
in an effort to to
in order to to
in relation to about, with, to
is applicable to applies to
maintain keep, support
modify change
notify tell
objective aim, goal
option choice, way
participate join
portion part
previous earlier
previously before
proceed do, start, try
proficiency skill
provide give, offer, say
provided that if
purchase buy
regarding about, of, on
relative to about, on
remain stay
require need
requirement need
retain keep
selection choice
submit give, send
subsequent later, next
subsequently after, later, then
substantial large, much
successfully complete complete, pass
sufficient enough
therefore so
time period time, period
utilize use
utilization use

Hopefully this gives you a sense of the attention to detail in the work, as well as some insight into the way a large team can work together to produce something with a singular voice.

What questions do you have?

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