Fraction Forest

Introduce the idea. Luna opens with the fracpie visual — a fraction as a pie and a bar: k of n parts shaded, across 3 narrated beats, so the concept is seen before it is ever practised.

What Luna says

• A fraction is a piece of a whole. Imagine cutting a pizza into four equal slices.
• Now take three of those four slices — that is three-quarters.
• The bottom number, four, says how many equal parts. The top number, three, says how many we have.

In the open config

id: slice
label: Slices
beats:
  - say: lfr-1
    caption: A fraction is a piece of a whole. Imagine cutting a pizza into four equal slices.
    view:
      kind: fracpie
      key: q14
      k: 1
      "n": 4
  - say: lfr-2
    caption: Now take three of those four slices — that is three-quarters.
    view:
      kind: fracpie
      key: q34
      k: 3
      "n": 4
  - say: lfr-3
    caption: The bottom number, four, says how many equal parts. The top number, three, says how many we have.
    view:
      kind: fracpie
      key: q34
      k: 3
      "n": 4

Preview

Worked example. Luna walks one case step by step with the fracpie view — a fraction as a pie and a bar: k of n parts shaded, turning the idea into a procedure a child can repeat.

What Luna says

• Here is one-half — just one of two equal parts.

In the open config

id: half
label: One-half
beats:
  - say: lfr-4
    caption: Here is one-half — just one of two equal parts.
    view:
      kind: fracpie
      key: q12
      k: 1
      "n": 2

Preview

Your turn. The lesson hands off to the practice board: the child now answers, applying what the fracbar visual — a fraction bar split into n parts with k shaded just showed.

What Luna says

• Bottom tells the equal parts, top tells how many you have. You try!

In the open config

id: go
label: Your turn
beats:
  - say: lfr-5
    caption: Bottom tells the equal parts, top tells how many you have. You try!
    view:
      kind: fracbar
      key: fb34
      "n": 4
      k: 3

Preview

Introduce the idea. Luna opens with the equiv visual — equivalent fractions: a/b scaled by m to show why they are equal, across 3 narrated beats, so the concept is seen before it is ever practised.

What Luna says

• Equivalent fractions look different but are exactly the same amount. Watch one-half.
• Slice each half into two — now it reads two-quarters, but the shaded part is the same!
• The trick is to multiply the top and the bottom by the same number.

In the open config

id: half
label: Half
beats:
  - say: leq-1
    caption: Equivalent fractions look different but are exactly the same amount. Watch one-half.
    view:
      kind: equiv
      key: eq12
      a: 1
      b: 2
      m: 2
  - say: leq-2
    caption: Slice each half into two — now it reads two-quarters, but the shaded part is the same!
    view:
      kind: equiv
      key: eq12
      a: 1
      b: 2
      m: 2
  - say: leq-3
    caption: The trick is to multiply the top and the bottom by the same number.
    view:
      kind: equiv
      key: eq12
      a: 1
      b: 2
      m: 2

Preview

Worked example. Luna walks one case step by step with the equiv view — equivalent fractions: a/b scaled by m to show why they are equal, turning the idea into a procedure a child can repeat.

What Luna says

• One-third becomes two-sixths the very same way.

In the open config

id: third
label: Third
beats:
  - say: leq-4
    caption: One-third becomes two-sixths the very same way.
    view:
      kind: equiv
      key: eq13
      a: 1
      b: 3
      m: 2

Preview

Your turn. The lesson hands off to the practice board: the child now answers, applying what the equiv visual — equivalent fractions: a/b scaled by m to show why they are equal just showed.

What Luna says

• Multiply top and bottom by the same number and the value never changes. You try!

In the open config

id: go
label: Your turn
beats:
  - say: leq-5
    caption: Multiply top and bottom by the same number and the value never changes. You try!
    view:
      kind: equiv
      key: eq12b
      a: 1
      b: 2
      m: 3

Preview

Introduce the idea. Luna opens with the compfrac visual — two fractions side by side (k1/n1 vs k2/n2) for comparing, across 2 narrated beats, so the concept is seen before it is ever practised.

What Luna says

• To compare fractions, picture the pieces. Which is bigger: one-half or one-third?
• Same one slice, but halves are bigger than thirds — so one-half is more.

In the open config

id: pieces
label: Piece size
beats:
  - say: lcf-1
    caption: "To compare fractions, picture the pieces. Which is bigger: one-half or one-third?"
    view:
      kind: compfrac
      key: c1213
      k1: 1
      n1: 2
      k2: 1
      n2: 3
  - say: lcf-2
    caption: Same one slice, but halves are bigger than thirds — so one-half is more.
    view:
      kind: compfrac
      key: c1213
      k1: 1
      n1: 2
      k2: 1
      n2: 3

Preview

Worked example. Luna walks one case step by step with the compfrac view — two fractions side by side (k1/n1 vs k2/n2) for comparing, turning the idea into a procedure a child can repeat.

What Luna says

• When the bottoms match, just compare the tops. Three-fifths beats two-fifths.

In the open config

id: samebottom
label: Same bottom
beats:
  - say: lcf-3
    caption: When the bottoms match, just compare the tops. Three-fifths beats two-fifths.
    view:
      kind: compfrac
      key: c3525
      k1: 3
      n1: 5
      k2: 2
      n2: 5

Preview

Your turn. The lesson hands off to the practice board: the child now answers, applying what the compfrac visual — two fractions side by side (k1/n1 vs k2/n2) for comparing just showed.

What Luna says

• Bigger pieces, or more pieces — picture it. You try!

In the open config

id: go
label: Your turn
beats:
  - say: lcf-4
    caption: Bigger pieces, or more pieces — picture it. You try!
    view:
      kind: compfrac
      key: c1214
      k1: 1
      n1: 2
      k2: 1
      n2: 4

Preview

Introduce the idea. Luna opens with the addfrac visual — adding fractions with a like denominator: a/n + b/n, across 2 narrated beats, so the concept is seen before it is ever practised.

What Luna says

• To add fractions with the same bottom, we just add the tops. One-quarter plus two-quarters.
• One piece plus two pieces is three pieces — three-quarters. The bottom stays the same!

In the open config

id: like
label: Same bottom
beats:
  - say: laf-1
    caption: To add fractions with the same bottom, we just add the tops. One-quarter plus two-quarters.
    view:
      kind: addfrac
      key: a124
      a: 1
      b: 2
      "n": 4
  - say: laf-2
    caption: One piece plus two pieces is three pieces — three-quarters. The bottom stays the same!
    view:
      kind: addfrac
      key: a124
      a: 1
      b: 2
      "n": 4

Preview

Worked example. Luna walks one case step by step with the addfrac view — adding fractions with a like denominator: a/n + b/n, turning the idea into a procedure a child can repeat.

What Luna says

• Another one: two-fifths plus one-fifth makes three-fifths.

In the open config

id: like2
label: Another
beats:
  - say: laf-3
    caption: "Another one: two-fifths plus one-fifth makes three-fifths."
    view:
      kind: addfrac
      key: a215
      a: 2
      b: 1
      "n": 5

Preview

Worked example. Luna walks one case step by step with the equiv view — equivalent fractions: a/b scaled by m to show why they are equal, turning the idea into a procedure a child can repeat. It also draws on addfrac.

What Luna says

• What if the bottoms are different, like one-half plus one-quarter? First we make them match.
• Change one-half into two-quarters. Now two-quarters plus one-quarter is three-quarters.

In the open config

id: unlike
label: Make them match
beats:
  - say: laf-4
    caption: What if the bottoms are different, like one-half plus one-quarter? First we make them match.
    view:
      kind: equiv
      key: eqm
      a: 1
      b: 2
      m: 2
  - say: laf-5
    caption: Change one-half into two-quarters. Now two-quarters plus one-quarter is three-quarters.
    view:
      kind: addfrac
      key: a214
      a: 2
      b: 1
      "n": 4

Preview

Your turn. The lesson hands off to the practice board: the child now answers, applying what the addfrac visual — adding fractions with a like denominator: a/n + b/n just showed.

What Luna says

• Same bottoms: add the tops. Different bottoms: make them match first. You try!

In the open config

id: go
label: Your turn
beats:
  - say: laf-6
    caption: "Same bottoms: add the tops. Different bottoms: make them match first. You try!"
    view:
      kind: addfrac
      key: a124b
      a: 1
      b: 2
      "n": 4

Preview

Introduce the idea. Luna opens with the addfrac visual — adding fractions with a like denominator: a/n + b/n, across 2 narrated beats, so the concept is seen before it is ever practised.

What Luna says

• To add fractions with the same bottom, we just add the tops. One-quarter plus two-quarters.
• One piece plus two pieces is three pieces — three-quarters. The bottom stays the same!

In the open config

id: like
label: Same bottom
beats:
  - say: laf-1
    caption: To add fractions with the same bottom, we just add the tops. One-quarter plus two-quarters.
    view:
      kind: addfrac
      key: a124
      a: 1
      b: 2
      "n": 4
  - say: laf-2
    caption: One piece plus two pieces is three pieces — three-quarters. The bottom stays the same!
    view:
      kind: addfrac
      key: a124
      a: 1
      b: 2
      "n": 4

Preview

Worked example. Luna walks one case step by step with the addfrac view — adding fractions with a like denominator: a/n + b/n, turning the idea into a procedure a child can repeat.

What Luna says

• Another one: two-fifths plus one-fifth makes three-fifths.

In the open config

id: like2
label: Another
beats:
  - say: laf-3
    caption: "Another one: two-fifths plus one-fifth makes three-fifths."
    view:
      kind: addfrac
      key: a215
      a: 2
      b: 1
      "n": 5

Preview

Worked example. Luna walks one case step by step with the equiv view — equivalent fractions: a/b scaled by m to show why they are equal, turning the idea into a procedure a child can repeat. It also draws on addfrac.

What Luna says

• What if the bottoms are different, like one-half plus one-quarter? First we make them match.
• Change one-half into two-quarters. Now two-quarters plus one-quarter is three-quarters.

In the open config

id: unlike
label: Make them match
beats:
  - say: laf-4
    caption: What if the bottoms are different, like one-half plus one-quarter? First we make them match.
    view:
      kind: equiv
      key: eqm
      a: 1
      b: 2
      m: 2
  - say: laf-5
    caption: Change one-half into two-quarters. Now two-quarters plus one-quarter is three-quarters.
    view:
      kind: addfrac
      key: a214
      a: 2
      b: 1
      "n": 4

Preview

Your turn. The lesson hands off to the practice board: the child now answers, applying what the addfrac visual — adding fractions with a like denominator: a/n + b/n just showed.

What Luna says

• Same bottoms: add the tops. Different bottoms: make them match first. You try!

In the open config

id: go
label: Your turn
beats:
  - say: laf-6
    caption: "Same bottoms: add the tops. Different bottoms: make them match first. You try!"
    view:
      kind: addfrac
      key: a124b
      a: 1
      b: 2
      "n": 4

Preview

Introduce the idea. Luna opens with the big visual — a single big numeral or label, for emphasis / answer-reveal beats, across 2 narrated beats, so the concept is seen before it is ever practised.

What Luna says

• A mixed number is a whole number and a fraction together — like one and a half.
• One whole, plus one-half of another, makes one and a half.

In the open config

id: what
label: A whole + part
beats:
  - say: lmx-1
    caption: A mixed number is a whole number and a fraction together — like one and a half.
    view:
      kind: big
      key: m1
      text: 1½
      color: "#4ade80"
  - say: lmx-2
    caption: One whole, plus one-half of another, makes one and a half.
    view:
      kind: big
      key: m1
      text: 1 + ½ = 1½
      color: "#4ade80"

Preview

Worked example. Luna walks one case step by step with the big view — a single big numeral or label, for emphasis / answer-reveal beats, turning the idea into a procedure a child can repeat.

What Luna says

• Two and three-quarters means two whole ones and three-quarter slices.

In the open config

id: more
label: Bigger
beats:
  - say: lmx-3
    caption: Two and three-quarters means two whole ones and three-quarter slices.
    view:
      kind: big
      key: m2
      text: 2¾
      color: "#4ade80"

Preview

Your turn. The lesson hands off to the practice board: the child now answers, applying what the fracbar visual — a fraction bar split into n parts with k shaded just showed.

What Luna says

• A whole number sitting next to a fraction — that is a mixed number. You try!

In the open config

id: go
label: Your turn
beats:
  - say: lmx-4
    caption: A whole number sitting next to a fraction — that is a mixed number. You try!
    view:
      kind: fracbar
      key: mx34
      "n": 4
      k: 3

Preview

Introduce the idea. Luna opens with the big visual — a single big numeral or label, for emphasis / answer-reveal beats, across 2 narrated beats, so the concept is seen before it is ever practised. It also draws on fracbar.

What Luna says

• Multiplying a fraction by a whole number is just repeated adding. Three times one-quarter.
• One-quarter, plus one-quarter, plus one-quarter — that is three-quarters.

In the open config

id: repeat
label: Repeated adding
beats:
  - say: lmw-1
    caption: Multiplying a fraction by a whole number is just repeated adding. Three times one-quarter.
    view:
      kind: big
      key: w1
      text: 3 × ¼
      color: "#22d3ee"
  - say: lmw-2
    caption: One-quarter, plus one-quarter, plus one-quarter — that is three-quarters.
    view:
      kind: fracbar
      key: fbw
      "n": 4
      k: 3

Preview

Worked example. Luna walks one case step by step with the big view — a single big numeral or label, for emphasis / answer-reveal beats, turning the idea into a procedure a child can repeat.

What Luna says

• So three times one-quarter is three-quarters. Just multiply the top by the whole number.

In the open config

id: result
label: The answer
beats:
  - say: lmw-3
    caption: So three times one-quarter is three-quarters. Just multiply the top by the whole number.
    view:
      kind: big
      key: w2
      text: 3 × ¼ = ¾
      color: "#22d3ee"

Preview

Your turn. The lesson hands off to the practice board: the child now answers, applying what the fracbar visual — a fraction bar split into n parts with k shaded just showed.

What Luna says

• Multiply the top by the whole number and keep the bottom. You try!

In the open config

id: go
label: Your turn
beats:
  - say: lmw-4
    caption: Multiply the top by the whole number and keep the bottom. You try!
    view:
      kind: fracbar
      key: fbw2
      "n": 4
      k: 3

Preview