Place Value Card Challenge

Overview

Students explore how the position of a digit changes its value by rearranging number cards and representing numbers with place-value materials. The lesson builds on counting, recognising numerals and grouping in tens; hundreds are introduced as an optional challenge rather than an expectation for every Year 1 student.

Learning intentions

• WALT build and read two-digit numbers using tens and ones.
• WALT explain how the position of a digit changes its value.
• WALT compare numbers made from the same digit cards.
• WALT use mathematical language and representations to explain our thinking.

Success criteria

• I can make a two-digit number from two cards.
• I can show how many tens and ones are in my number.
• I can rearrange the cards to make another number and say which is bigger.
• I can explain that a digit’s position tells us its value.

Curriculum links

• Number: recognising, representing and comparing numbers using place value.
• Number: grouping ones into tens and connecting numerals with concrete representations.
• Mathematical thinking: noticing patterns, making conjectures, comparing, explaining and justifying.
• Te Mātaiaho Mathematics and Statistics — Mathsteasers: developing higher-order thinking through number challenges and relevant mathematical content.

Lesson structure (30 minutes)

1. 0–5 min · Hook and number mystery. Open with the number mystery hook and display cards 2 and 4. Students turn and talk about numbers they could make; invite responses of 24 and 42, then build both with rods and ask why the same cards make different numbers. Explain that the position of a digit changes its value. Briefly show the 10 card as a stretch idea: when it is placed at the front in this challenge, it represents 100, so 10 and 4 can make 104—1 hundred, 0 tens and 4 ones.

2. 5–10 min · Teacher modelling. Use the modelling slides to model cards 3 and 7. Build 37 as 3 tens and 7 ones, then 73 as 7 tens and 3 ones. Think aloud: “The 7 moved into the tens place, so its value changed.” Model partner-check questions: “What number did you make?”, “How many tens?”, “How many ones?”, “Can you show it with rods?” and “Can you make another number using the same cards?” Briefly model 106 using the 10 card, making clear that this is an optional challenge.

3. 10–18 min · Partner challenge: two cards. Organise 17 students into eight pairs and one three-person group. Give each group number cards 1–10, number rods and, where useful, the place-value recording sheet. One student picks two cards, says them, arranges a two-digit number and builds it. They state the number of tens and ones, swap the cards, build the second number and compare them. Partners ask, “Which number is bigger? Why? What changed? What stayed the same?” If 10 is selected, support interested students to build 105 as 1 hundred, 0 tens and 5 ones; other students may redraw a card or continue with two-digit numbers.

4. 18–25 min · Partner challenge: three cards. Display the three-card challenge instructions. Students who are ready pick three cards and arrange them to make a hundreds number. For example, 3, 4 and 9 can make 349, 439, 493, 934 or 943. They build one number, then find the largest and smallest possible numbers and one number in between. Partners check each other using: “My number is ___. I have ___ hundreds, ___ tens and ___ ones.” Students still developing confidence continue with two cards and focus on tens and ones.

5. 25–28 min · Challenge and reasoning. Give selected students cards 2, 5 and 8 to build a number such as 258. Ask, “What would happen if the 8 moved to the hundreds place?” Compare 258 and 825, then compare 258 and 285. Encourage students to explain which place changed and why the number became larger or smaller. Record useful ideas on the comparison and reasoning slide.

6. 28–30 min · Plenary and exit question. Bring students together and ask, “What did we learn about the position of a digit?” Invite the response: “The position of a digit tells us how much it is worth.” Finish with cards 3, 6 and 9: students say or build the biggest and smallest numbers. Complete the final prompt on the reflection and exit question: “My number is ___. It has ___ tens and ___ ones.”

Resources

• the place-value card challenge slide deck
• the place-value recording sheet
• Number cards 1–10 for each pair
• Number rods or base-ten materials
• Hundreds, tens and ones place-value mats
• Board or chart paper and marker
• One teacher demonstration set of cards and rods

Assessment

• Listen for whether students can identify the tens and ones and notice that swapping cards changes place value.
• Observe models and partner explanations; ask individuals to justify which of two numbers is larger.
• Collect or quickly check the exit response for a correctly represented number and a place-value explanation. Note students needing further support with grouping tens or reading two-digit numbers.

Differentiation

• Support: begin with cards 1–5, use only two cards and provide a hundreds–tens–ones mat. Build the number alongside the student before asking for an explanation.
• Provide the sentence frame, “My number has ___ tens and ___ ones,” with visual examples and gesture-supported vocabulary for EAL learners.
• For students needing additional support, use a smaller selection of cards, allow repeated oral rehearsal and pair them with a patient mathematical talk partner.
• Extension: use three cards, find all possible numbers, order them from smallest to largest, or explore 104, 107 and 109 with the 10 card. Ask students to explain how changing one digit affects the whole number.