Architecture of Grace
Mathematics · Number Concepts & Data

Number Concepts & Data

Thirteen activities. Every one works on this screen or on paper — both count. Nothing you do leaves this computer unless you tap Send.

← Math, every band

Strand 1 · Fractions

What a fraction is

Before we ever add fractions, we learn what one IS. Cut things fairly, name the parts, and see where fractions live on the number line.

Cut It Fair

Cut a whole into equal parts. Fair shares are where every fraction begins.

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Top and Bottom

The bottom counts the parts. The top says how many you mean. Numerator and denominator, plainly.

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More Than a Whole?

Some fractions are smaller than 1. Some are exactly 1. Some spill over. Tell them apart.

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Close To What?

Every fraction lives near 0, near one-half, or near 1. Learn to feel which one.

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Which Is Bigger?

Compare fractions with circles and bars. The pictures decide — and sometimes they tie.

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Same Amount, New Name

One-half and two-fourths are the same amount wearing different names. Line the bars up and see it.

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Strand 2 · Data

Numbers that tell a story

A pile of numbers is just a pile until you organize it. Level it, order it, plot it — and it starts talking.

Make It Even

Move blocks between towers until they match. The even height is the mean — no formula needed yet.

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The Middle Number

Line the numbers up smallest to largest. The middle one is the median; the stretch is the range.

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The Odd One Out

One number sits far from the rest — and it drags the mean. Find it, and see what it does.

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Stems and Leaves

Sort two-digit numbers into stems and leaves, and a picture of the whole class appears.

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X Marks the Number

Stack an X for every answer and a line plot grows. Then let it answer your questions.

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Strand 3 · Whole Numbers

The operations that carry everything

Two rituals worth owning for life: take-away with trading, and long division. Both are walked one column at a time, with every move written — no number is too big for them.

Bring It Down

Long division as four small moves — divide, multiply, subtract, bring down — from one-digit divisors up to two digits into five-digit numbers.

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Trade a Ten

Column subtraction with regrouping — take what you can, trade when you can’t, zeros included, up to five-digit numbers.

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The words we're learning

Every word below is taught inside an activity — never as a list to memorize. This is just so you can see them all in one place.

Fractions
  • fair shares
  • fractional parts
  • numerator
  • denominator
  • benchmark
  • fraction bars
  • equivalent fractions
  • infinite
Data
  • average / mean
  • median
  • range
  • minimum
  • maximum
  • outlier
  • stem-and-leaf plot
  • stem · leaf
  • line plot
Whole numbers
  • dividend · divisor
  • quotient
  • remainder
  • regroup / trade
For the teacher

<b>The order is the pedagogy.</b> Activities 1–6 build the concept of a fraction before any operation on one; 7–11 build statistics from organizing data, not from formulas. Run them in order the first time; after that, any activity works as a warm-up or a re-probe.

<b>Every activity holds three sets</b> — the same skills with different numbers — so the same student can be probed three weeks running without being measured on memory. The teacher panel at the bottom of each page builds the probe row (independent · supported · hints · confidence) for you.

1

<b>Send a link, get a row back.</b> Share any activity's address with a student (or show it on the board). When the page can reach your Sheet, a Send button appears after a finished set — one tap posts one row to the <b>Practice</b> tab of your Google Sheet: activity, set, independent, supported, hints, confidence, and the first name the student types. Nothing else ever travels.

2

<b>A bare link stays private.</b> On a device with no path to your Sheet, the Send button never appears and the page is exactly what it says: nothing leaves the computer. The lock section on every page tells the student the truth for the mode it is in.

<b>Every activity in this series — and every Social Studies activity — opens three doors.</b> A student who wants to see one first taps <b>Show me one first</b> and the page walks a worked example at their pace — watching is instruction, never a trial. The eight problems are the middle door. And after the close card, <b>One more, if you want it</b> offers a single honest stretch — optional every time, and declining is named as a strong move too. The probe row records all three (demo watched · 8-count · stretch), so one page serves your lowest and your highest learner without either being singled out. (The Interior Math and Science Vocabulary pages open the first two doors — the worked example and the set — not yet the stretch.)

<b>Confidence is never a score.</b> The 1–5 at the end of each activity is the student's own read of themselves. It goes in the row so you can watch it move — it is never averaged with anything.

Standards alignment

This series serves a small self-contained class, so the anchors span grade levels on purpose — each code names the concept’s home in the Common Core, not a grade-level claim about the students working on it.

c1Cut It Fair — CCSS 3.G.A.2 · 3.NF.A.1
c2Top and Bottom — CCSS 3.NF.A.1
c3More Than a Whole? — CCSS 4.NF.B.3c
c4Close To What? — CCSS 4.NF.A.2 (benchmarks)
c5Which Is Bigger? — CCSS 4.NF.A.2
c6Same Amount, New Name — CCSS 4.NF.A.1
c7Make It Even — CCSS 6.SP.B.5c (mean)
c8The Middle Number — CCSS 6.SP.B.5c (median)
c9The Odd One Out — CCSS 6.SP.B.5c (mode & outliers)
c10Stems and Leaves — CCSS 6.SP.B.4
c11X Marks the Number — CCSS 6.EE.B.5
c12Bring It Down — CCSS 6.NS.B.2 (builds from 4.NBT.B.6)
c13Trade a Ten — CCSS 3.NBT.A.2 (regrouping)