Grades 1 to 6
216 weeks
Print and go

The math of
how things connect.

Six complete school years of sorting, maps, proofs, routes and rules, one weekly assignment at a time. Discrete mathematics needs very little computational fluency, which is exactly why it works as enrichment: a student still shaky on regrouping can reason well about a map coloring, and be asked to prove it.

Each year teaches one new mathematical move. Read them in order and they make a sentence: sort it, see it, count it, rule it out, cost it, generalize it.

Pip, a friendly character drawn as a vertex with five edges

Meet Pip

One dot, five lines. Pip is a graph: the exact object the students spend six years proving things about.

6
school years
Grades 1 to 6
216
weekly assignments
two pages each
101
CA standards touched
reinforced, not replaced
$0
prep cost
photocopy and go

One move a year

six books.
One argument.

The years are not the same year with bigger numbers. Grade 1 asks a child to hold a rule in their head while they use it. Grade 2 shows them that mathematics has parts that are not arithmetic. Each year after that adds a different kind of move and reuses the same objects, shapes, graphs, maps, coins and codes, as material for it. That order is also the order in which the moves are hard: a first grader can follow a rule, a third grader can be systematic, a sixth grader can hold a variable.

Why this, why now

Elementary math is about quantity.
This is about structure.

Discrete mathematics asks how things connect, how many arrangements exist, and whether something is possible at all. Because it leans on reasoning rather than computation, it reaches students that arithmetic practice leaves behind, and it stretches the ones who finish early.

It gives them proof

A whole year of the line, Grade 4, is about things that cannot be done: two colors will not work, five dots cannot each have three lines, the bridge walk is impossible. Explaining why is a kind of thinking the regular curriculum rarely asks for at this age.

It feeds the pacing guide

Loops are repeated addition. Grids are arrays. Binary is place value. Factor rectangles are 4.OA.4 in disguise, and some students arrive at arrays through the loop who never got there through the array.

It needs almost nothing

Crayons, counters and a photocopier. No devices, no kits, no subscription, no training week before you can start.

It is checked, not asserted

Every one of the 2,231 numeric answers in the 6 newest teacher guides is recomputed from the problem as the workbook states it, by a script that ships with the source and runs on every build. If a fix to a page changes an answer, the build fails until the guide agrees.

Questions

What teachers ask.

Anything not answered here is worth an email. We would rather field the question than have a school guess.

No. It sits beside it. Every year is sequenced against a typical California pacing guide so each week lands near the standard the class is already teaching, and every assignment names that standard on the page.

Pilot a classroom

One teacher.
One year.
No cost.

We are placing these years in elementary classrooms across the San Gabriel Valley. A pilot is one teacher, one class, one school year, materials and support provided. No year has been run start to finish yet, and the first teacher to do it will change how every later book gets written.

Pip celebrating