Build Beyond One

Overview

Students use fraction tiles to add and subtract fractions with the same denominator. They connect concrete models to written improper fractions and mixed numbers, including totals greater than one, building on prior understanding that the denominator names the equal parts in one whole.

Learning intentions

• WALT add fractions with the same denominator.
• WALT subtract fractions with the same denominator.
• WALT model answers using fraction tiles.
• WALT record improper fractions as mixed numbers when the answer is greater than one.

Success criteria

• I can explain why the denominator stays the same when I add or subtract like fractions.
• I can use fraction tiles to show my calculation.
• I can write an answer as an improper fraction and, when needed, a mixed number.
• I can explain my thinking using words, pictures or equations.

Curriculum links

• Mathematics and Statistics — developing mathematical reasoning through a rich problem-solving challenge.
• Mathsteasers — higher-order thinking questions that deepen understanding for advanced learners.
• Mathsteasers alignment — connecting hands-on fraction models with relevant mathematical ideas and written representations.
• Communication and representation — explaining strategies and showing mathematical thinking in more than one way.

Lesson structure (30 minutes)

1. 0–4 min · Hook and notice. Teacher displays the question “Is 3/8 + 3/8 + 3/8 equal to 9/8 or 1 1/8?” using the opening fraction challenge slide and invites students to make a silent prediction before sharing with a partner. Students explain what they notice about the numerator and denominator and identify which answer they think is correct.

2. 4–9 min · Model the idea. Teacher gives each pair a fraction wall or tiles from the Fraction Wall and Strip Cards and models placing three eighths together: 3/8 + 3/8 + 3/8 = 9/8. Show that eight eighths make one whole, leaving one eighth, so 9/8 = 1 1/8; reinforce that the denominator remains eight because the parts are still eighths. Students build the example, count the eighths and record both forms in their books.

3. 9–15 min · Guided addition. Teacher displays the guided examples on the worked-example and guided-practice slides: 2/6 + 3/6, 4/8 + 5/8 and 3/10 + 8/10. Prompt students to first build, then add the numerators, check whether they have made a whole, and record an improper fraction and mixed number where appropriate. Students solve each example with their partner, showing the tiles before writing the equation.

4. 15–21 min · Guided subtraction. Teacher models 11/8 − 3/8 by building 11 eighths, removing three eighths and regrouping the eight remaining eighths as one whole; connect 8/8 = 1 and 11/8 = 1 3/8. Use the subtraction modelling slides to present 7/6 − 2/6 and 13/10 − 5/10, asking, “What changes? What stays the same?” Students use tiles to solve, then explain how subtracting numerators gives the number of parts left.

5. 21–27 min · Independent practice. Teacher distributes the same-denominator fractions practice worksheet and reminds students to follow the routine: build it, draw or describe it, write the improper fraction, then convert to a mixed number if greater than one. Circulate and ask selected students to justify why their denominator has not changed. Students complete the core addition and subtraction questions independently, using tiles when needed, then compare one answer with a partner.

6. 27–30 min · Share and exit check. Teacher uses the discussion and exit-question slides to revisit the hook and asks students to solve 5/8 + 6/8 and explain the answer to a partner. Students complete the exit response: “Show 5/8 + 6/8 with a model. Write the answer as an improper fraction and a mixed number. Explain why the denominator stays eight.”

Resources

• the fraction modelling and discussion slide deck
• the same-denominator fractions practice worksheet
• the Fraction Wall and Strip Cards
• Fraction tiles or equivalent fraction strips for each pair
• Mini-whiteboards and pens
• Mathematics books and pencils
• Prepared exit-question display

Assessment

• Observe whether students combine or remove only the numerators while retaining the common denominator.
• During guided practice, check that students can identify eight eighths, six sixths or ten tenths as one whole and regroup beyond one.
• Collect the worksheet and exit response, looking for accurate models, improper fractions and mixed-number conversions.

Differentiation

• Support students by pairing them strategically, leaving fraction tiles available, and providing the sentence frame: “The denominator stays ___ because each part is a ___.”
• Use smaller denominators such as halves, thirds, quarters or sixths for students who need confidence before working with eighths and tenths.
• For students ready for challenge, ask them to create two different same-denominator calculations equal to 1 1/4, including one addition and one subtraction, and prove each with tiles.
• Accept oral explanations, drawings or equations alongside written responses; pre-teach “numerator”, “denominator”, “improper fraction” and “mixed number” with gestures and examples for EAL learners.