ProgramsDiscrete Math Adventures
Grade 2
36 weeks
Print and go

THE MATH OF
HOW THINGS CONNECT.

A full year of maps, robots, secret codes and bridges, for seven-year-olds. Discrete mathematics needs almost no computational fluency, which is exactly why it works as enrichment. A student still shaky on regrouping can reason beautifully about a map coloring, and be asked to prove 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 the year proving things about.

36
weekly assignments
one full school year
30–40
minutes each
two pages, front and back
20
CA standards touched
reinforced, not replaced
$0
prep cost
photocopy and go

Why this, why now

SECOND GRADE 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

Three weeks of the year end in something being impossible: two colors cannot work, five dots cannot each have three lines, the bridge walk cannot be done. 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. Weeks 32 through 35 are 2.OA.4 and 2.G.2 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.

Six strands, 36 weeks

WHAT WE TEACH.
WEEK BY WEEK.

The strands interleave rather than run in blocks, so an idea comes back three or four times across the year with more weight each time.

Weeks 1–4, 13, 25

SORTING & LOGIC

Rules, Venn diagrams, logic grids, and the difference between an example and a reason. This is where a child first has to defend an answer instead of just giving one.

  • Inferring a rule from examples and non-examples
  • Two-attribute sorting
  • Deduction on a logic grid
  • Always / sometimes / never
Weeks 5–8, 10, 11

NUMBER STRUCTURE

Binary as place value with a different multiplier, function machines, sorting algorithms, and binary search. Arithmetic seen from the outside.

  • Base two as a second place-value system
  • Input–rule–output machines
  • Two sorting methods compared
  • Halving to find a hidden number
Weeks 12, 15, 29, 33, 34

COUNTING CAREFULLY

Counting every case without missing one or repeating one. Handshakes, combinations, choice trees, tilings, and lattice paths, organized listing as a discipline.

  • Systematic enumeration
  • The double-counting correction
  • Arrays as a picture of a count
  • Pascal’s triangle, built by hand
Weeks 17, 18, 23

MAPS & COLORS

Graph coloring, and the moment a child proves that fewer colors is not merely hard but impossible. Ends with the Four Color Theorem, by name.

  • Coloring with a shared-border constraint
  • Finding the structure that forces a third color
  • Reading a graph as dots and edges
  • Building a bar graph from graph data
Weeks 9, 16, 26, 27, 28

PATHS & ROUTES

Shortest paths, Euler tracing, the Bridges of Königsberg, and connecting towns for the least cost. Heavy grade-level addition, wrapped around real theorems.

  • Weighted shortest path
  • Odd and even used as a working tool
  • Why the bridge walk is impossible
  • Minimum spanning trees
Weeks 20, 21, 22, 32, 35, 36

ALGORITHMS & CODES

Instructions precise enough for a machine: robot programs, loops as repeated addition, greedy change-making, clock arithmetic, and ciphers.

  • Writing and shortening a program
  • Loops as repeated addition
  • A greedy rule, and where it fails
  • Shift ciphers and binary decoding

Anatomy of a week

TWO PAGES.
FIVE MOVES.

01

In class this week

A line naming the standard the class is already working on, so the sheet reinforces Tuesday’s lesson.

02

Number Warm-Up

Two minutes of ordinary grade-level fluency. The page starts on familiar ground.

03

The Adventure

The main activity, with every map, grid, and diagram printed on the page, nothing to prepare.

04

Talk About It

One question answered out loud. Most weeks have short answers and long reasons.

05

★ Challenge Zone

Genuinely harder, and not expected of everyone. Where the student who finishes in eight minutes goes.

CALIFORNIA STANDARDS TOUCHED

This is enrichment: it reinforces and extends these standards rather than delivering them. No standard here is taught to mastery by this program alone.

2.OA.12.OA.22.OA.32.OA.42.NBT.12.NBT.22.NBT.32.NBT.42.NBT.52.NBT.72.MD.12.MD.42.MD.52.MD.62.MD.72.MD.82.MD.102.G.12.G.22.G.3

What a school receives

THE MATERIALS.

Student workbook

77 printable pages

Cover, how-to, a year-at-a-glance spread, 36 two-page assignments, and a certificate. Proofed in grayscale.

Teacher guide

every week, every answer

Answer keys for the activity, the practice set, and the Challenge Zone, plus a running note and the standards tie for all 36 weeks.

Classroom kit

crayons, counters, number cards

The only physical materials the year asks for. Most classrooms already have them.

Everything is free to download

Questions

WHAT TEACHERS ASK.

No. It sits beside it. The year is sequenced against a typical California Grade 2 pacing guide so that each week’s puzzle lands near the standard the class is already teaching, money week on coin counting, time week on clock arithmetic, the array weeks at the end where multiplication begins.

Pilot a classroom

ONE TEACHER.
ONE YEAR.
NO COST.

We are placing Discrete Math Adventures in Grade 2 classrooms across the San Gabriel Valley. A pilot is one teacher, one class, one school year, materials and support provided. Tell us about your school and we will send the adoption packet.

Pip celebrating