Fraction Match and Build

Overview

Students explore unit fractions as equal parts of a whole, then represent and combine them to make larger parts (including halves, quarters and eighths). The lesson uses concrete/cut-and-reassemble ideas and whiteboard practice to build fluency and understanding.

Learning intentions

Students will:

• recognise unit fractions as equal parts (½, ¼, 1/8) and explain what the “one part” means
• represent ½, ¼ and 1/8 in different ways (area models, sets of objects, and fraction notation)
• combine fractions with the same denominator to complete a whole or a larger whole (e.g. 2/8, 4/8)
• use reasoning to justify answers using diagrams and counts

Success criteria

Students can:

• correctly show ½, ¼ and 1/8 as equal parts of a whole (not “unequal pieces”)
• match a fraction to a representation and write the matching fraction notation
• combine parts with the same denominator to make a whole (e.g. 4/8 = ½, 8/8 = 1)
• explain their thinking using “each part is the same size” and “I can count the parts”

Curriculum links

• Number — recognise and represent unit fractions including ½, ¼ and 1/8 and their multiples in different ways; combine fractions with the same denominator to complete the whole
• Using mathematical modelling through representations (diagrams/manipulatives) to interpret and communicate fraction solutions
• Students communicate their strategies using diagrams, part-whole reasoning and counting

Lesson structure (90 minutes)

1. 0–10 min · Hook (equal parts). Teacher shows a paper strip (or rectangle) divided into 8 equal parts, with 1 part shaded, then asks: “How can we describe this in fraction words and symbols?” Students do a quick think-pair-share, then hold up mini whiteboards with “1/8” and one sentence: “one equal part out of 8.”

2. 10–25 min · Direct teach (unit fraction meaning). Teacher models cutting/reassembling: show a whole, then create halves, quarters, and eighths using the same size rule. Emphasise: “Unit fractions are equal parts of a whole.” Students follow along with a prepared fraction mat: trace over one half, one quarter and one eighth in turn, and write the fraction notation beside each.

3. 25–35 min · Whiteboard routine 1 (identify). Teacher displays 6 representations (area grids or circles) and calls out fractions in mixed order (½, ¼, 1/8). Students draw a matching mark and write the symbol: “Show me the part that is 1/8” (or ½ / ¼). Teacher circulates and checks accuracy.

4. 35–55 min · Group activity 1 (make bigger parts). Teacher forms 2 groups per class (swap groups halfway if required). Each group has: fraction cards (1/8, 2/8, 3/8, 4/8, 1/4, 1/2), an 8-part grid mat, and counters.

• Task: “Build ½ using eighths. Show how you know.” Students place counters/colour parts to represent required fractions (e.g. 4 of 8 parts for ½), then record a matching equation: 4/8 = 1/2.

5. 55–70 min · Whiteboard practice 2 (combine same denominator). Teacher gives number-of-parts prompts without using improper pieces, e.g. “Show 2/8.” “What is 4/8?” “What is 8/8?” “Is 6/8 equal to 3/4 (explain)?” Students work individually on whiteboards for 2 minutes per prompt, then teacher calls 2–3 students to show their diagram and explain.

6. 70–80 min · Short teach (link halves/quarters to eighths). Teacher highlights connections:

• 1/8 is one part of 8
• 2/8 makes 1/4
• 4/8 makes 1/2
• 8/8 makes 1 Students copy the key relationships to a “Quick Facts” page and underline the part-whole reasoning words.

7. 80–89 min · Group activity 2 (slide deck challenge). Teacher projects a slide with 2 tasks per group (teacher-stated time limit, e.g. 4 minutes each):

• Task A: “Represent 3/8 using the 8-part grid. Write it as a fraction.”
• Task B: “Represent 1/4 using eighths, then combine to show the whole when appropriate.” Students use the slide prompts to draw on whiteboards (or the group mat if provided), then show one answer per group to the teacher for quick verification.

8. 89–90 min · Exit ticket (quick check). Students answer on paper (or mini whiteboard):

• “Draw and label 1/8. How many 1/8 parts make 1/2?”
• “Combine: 4/8 = ____.”

Resources

• Fraction mats: 8-part grids (and some halves/quarters templates)
• Coloured pencils or markers
• Mini whiteboards, pens, erasers (one per student)
• Fraction cards (½, ¼, 1/8, 2/8, 3/8, 4/8, 8/8)
• Counters or small cubes
• Projector/slides with 8-part representations and prompt images
• Paper strips/rectangles for cutting demo (teacher use) and reassembly pieces (optional)
• Quick Facts sheet for students

Assessment

• Formative checks during whiteboard routine 1 and 2: accuracy of shaded/equal parts and correct fraction symbols
• Teacher observation in group activities: whether students combine same-denominator fractions by counting equal parts
• Exit ticket: correctness of “how many 1/8 make 1/2” and “4/8 equals what”

Differentiation

• Support: provide sentence starters on the board: “Each part is equal because…”, “I counted ___ parts out of 8.” Offer a partially labelled 8-part grid for students who need structure.
• Support for misconceptions: if a student shades uneven parts, pause and re-demonstrate equal-size partitioning before continuing.
• Extension: ask students to explain equivalence using diagrams (e.g. “How can you show 1/4 using eighths?”) and to create one “challenge question” for a partner (choose a fraction, represent it, and ask what it equals).
• EAL/SEN: use visual cues consistently (same 8-part model for all fractions), and accept oral explanations alongside written fraction notation.