Compare Numbers to 120

Overview

In this third lesson of Number Sentences Make Sense, students compare whole numbers to 120 and decide whether comparison sentences are true or false. They use place-value equipment, hundred boards and open number lines to explain the meaning of >, < and =.

Learning intentions

• WALT compare two whole numbers to 120.
• WALT use >, < and = correctly in comparison sentences.
• WALT justify a comparison using tens and ones or a number line.
• WALT check whether a number sentence is true or false.

Success criteria

• I can compare two numbers to 120.
• I can choose the correct comparison symbol.
• I can explain my decision using tens and ones.
• I can show or check my thinking on a number line.

Curriculum links

• Mathematics and Statistics — Number: recognise, represent and compare whole numbers using place value.
• Mathematics and Statistics — Mathematical practices: reason, represent, communicate and justify mathematical thinking.
• Te Mātaiaho Mathematics and Statistics — Mathsteasers: use higher-order thinking questions to deepen understanding.
• Mathsteasers alignment: connect challenging number problems with familiar mathematical learning.

Lesson structure (60 minutes)

1. 0–10 min · Place-value warm-up. Display the warm-up sequence in the place-value warm-up slides and build numbers such as 34, 70, 105 and 119 with tens and ones equipment; students make each number, say it aloud and identify its tens and ones. Ask, “Which is greater: 4 tens or 7 tens?” and “What does the 0 in 105 tell us?” Briefly revisit that numbers are organised into hundreds, tens and ones, and that the position of a digit affects its value.

2. 10–25 min · Explicit teaching. Use the comparison teaching slides to model comparing 47 and 74. Think aloud: “First I compare the tens. Seven tens is greater than four tens, so 74 is greater.” Introduce the symbols as comparison signs and read the sentence in both directions: 47 < 74 and 74 > 47. Model equal numbers, numbers with the same tens, and numbers over 100, such as 108 and 114. Build pairs with equipment, locate them on an open number line, and test the deliberately incorrect sentence 16 > 60. Students turn and talk: “Is it true or false? How do you know?” Emphasise that 16 has one ten and 60 has six tens, so 16 < 60.

3. 25–30 min · Station instructions. Show the three station tasks on the station instruction slides. Demonstrate how to record a comparison and an explanation on the compare numbers recording sheet. Place students in four groups of five and explain that each group will complete two or more tasks, rotating when signalled. Students rehearse the sentence frame: “___ is ___ than ___ because it has ___ tens/ones.”

4. 30–50 min · Comparison stations. At the place-value station, students make two teacher-provided numbers with tens, ones and, where needed, a hundred; they compare the models and record the sentence. At the hundred-board station, they locate two numbers, describe which is further along, and use the correct symbol. At the open-number-line station, they mark two numbers and explain which is further to the right. At the teacher station, support students with numbers below 50 before progressing to larger numbers. Students complete selected tasks on the compare numbers recording sheet, checking each other’s symbols and explanations. Circulate and ask, “What did you compare first?” and “How does your model prove it?”

5. 50–60 min · Reflection and exit check. Return to the reflection slides and revisit 16 > 60. Invite pairs to explain why it is false using either tens and ones or a number line. Students complete the final two questions on the compare numbers recording sheet: compare 89 and 98, then compare 107 and 107 and explain the symbol used. Take responses from several students, address any reversed symbols, and restate the key idea: compare the greatest place value first; if it is equal, compare the next place.

Resources

• the complete comparison number slide deck
• the compare numbers recording sheet
• Place-value blocks or bundled tens and ones
• Hundred boards, one per pair
• Open number lines to 120
• Number cards from 0 to 120
• Pencils, felt pens and mini-whiteboards
• Station labels and a timer

Assessment

• During the warm-up, check whether students identify the value of digits in the tens and ones places.
• At stations, listen for explanations based on place value rather than visual size or counting alone; record students needing further support.
• Use the final worksheet questions to assess accurate symbol use and the ability to justify a comparison.

Differentiation

• Support learners with place-value blocks, visual symbol cards, a large open number line and numbers below 50. Ask them to compare the tens first, then the ones.
• Provide the sentence frame: “___ is ___ than ___ because ___.” Allow students to explain orally, point to a model or draw their thinking before writing.
• Use a teacher-led small group for students who confuse the direction of the symbols. Physically turn the symbol card and read the complete sentence together.
• For advanced learners, provide sets of three or four numbers to order, invite them to generate true and false comparison sentences, and ask them to explain how changing one digit changes the comparison.