Discrete mathematicsGrade 2
Grade 2
36 weeks
77 pages

DISCRETE MATH ADVENTURES

SEE IT. THESE OBJECTS EXIST, AND THEY ARE INTERESTING.

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.

Download the workbook Teacher guide
36
weekly assignments
two pages each
77
printable pages
proofed in grayscale
19
CA standards touched
named on the page each week
$0
cost to a school
photocopy and go

Every week, in order

THE WHOLE YEAR.

Wk
Strand
Assignment
What the week is
01
Sorting & Logic
What’s My Rule?
Every group has a rule. Your job is to find it.
02
Sorting & Logic
Two Circles, One Middle
Where two groups overlap.
03
Number Structure
Pair Them Up
Even and odd, by pairing, not by memorizing.
04
Sorting & Logic
Always, Sometimes, Never
Mathematicians do not just answer. They prove.
05
Number Structure
How Computers Count
Two symbols, 0 and 1, are enough for every number.
06
Number Structure
Number Machines
Feed a number in. A rule changes it. What comes out?
07
Number Structure
Put Them in Order
Two ways to sort, and one is less work.
08
Sorting & Logic
Twenty Questions
The fastest way to find a hidden number.
09
Paths & Routes
The Shortest Way to the Gold
The fastest route is almost never the straightest.
10
Number Structure
Magic Squares
Every row, every column, every diagonal, the same total.
11
Number Structure
Balance Puzzles
Whatever one side weighs, the other side weighs too.
12
Counting Carefully
The Handshake Problem
Everyone shakes hands once. How many handshakes?
13
Sorting & Logic
Detective Week
Everything from the first twelve weeks, in one case file.
14
Measuring & Comparing
Sorting by Length
The same method as Week 7, on something that is not a number.
15
Counting Carefully
Covering a Strip
Two tile shapes. Surprisingly many ways.
16
Measuring & Comparing
Two Ways Across the Park
Adding lengths to compare whole routes.
17
Maps & Colors
Color the Kingdom
Neighbors must never match.
18
Maps & Colors
When Three Colors Is Not Enough
A puzzle that took mathematicians 124 years.
19
Money & Time
How Many Ways to Make 15¢?
Counting every answer without missing one.
20
Money & Time
The Fewest Coins
A rule so simple a machine could follow it. Usually.
21
Money & Time
Clock Arithmetic
On a clock, numbers wrap around.
22
Money & Time
Getting Ready for the Party
Some jobs have to wait for others.
23
Data & Graphs
Dots and Lines
A picture of who is connected to whom.
24
Data & Graphs
Who Wins the Tournament?
Counting games without drawing every one.
25
Sorting & Logic
Puzzle Fair
A little of everything from Weeks 14 to 24.
26
Paths & Routes
Trace It Without Lifting
An old puzzle with a beautiful rule hiding inside.
27
Paths & Routes
The Bridges of the Old City
A walk that was never possible, and the proof.
28
Paths & Routes
Connecting the Towns
Every town joined, for the smallest possible cost.
29
Counting Carefully
Counting Routes
How many ways to walk to school?
30
Shapes & Parts
Guess My Shape
The Week 8 game, played with shapes.
31
Shapes & Parts
Cutting Fair Shares
Equal parts do not have to look the same.
32
Shapes & Parts
Filling a Rectangle
Rows and columns give the same total.
33
Counting Carefully
The Ice Cream Shop
Counting every choice, without missing one.
34
Counting Carefully
Choice Trees
The same counting, drawn as branches.
35
Algorithms & Codes
Program the Robot
Instructions precise enough for a machine to follow.
36
Algorithms & Codes
Secret Codes
The last week. Everything you learned, put to work.

This is the book’s own table of contents, read out of the source rather than retyped here. The fourth column is the line printed under the title on the student’s page.

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. The list is the set of codes actually named in the “In class this week” line across the 36 weeks, counted from the published book.

2.G.12.G.22.G.32.MD.12.MD.42.MD.52.MD.62.MD.72.MD.82.MD.102.NBT.12.NBT.22.NBT.42.NBT.52.NBT.72.OA.12.OA.22.OA.32.OA.4
Everything, free

This guide predates the checking script the four later books ship with, so its answers have been read rather than recomputed. Writing that check is on the list.

The year after
GRADE 3: COUNT EVERY WAY
Count it.

No year in this line has been run start to finish in a classroom yet. If you would be the first teacher to do it, we would like to hear from you.