Place Value Foundations

Overview

In this first lesson of “Maths Mastery for Year 4”, students begin using place value to understand how digits represent amounts. They connect tens and ones to tenths and hundredths using visual models (base-ten blocks/number lines) so they can name and represent decimals using correct notation.

Learning intentions

• Students will recognise that in a number, the position of a digit shows its value.
• Students will use place value to read and write four-digit numbers accurately.
• Students will extend place value understanding to tenths and hundredths using visual models.
• Students will represent decimals using appropriate decimal notation and explain what each digit means.

Success criteria

• I can explain what each digit means in a four-digit number using place value language.
• I can model a decimal (to two decimal places) using tenths and hundredths.
• I can write a decimal in standard form (e.g., 0.25) and name it correctly.
• I can match a model to its decimal notation and explain my reasoning.

Curriculum links

• Number — recognise and extend the application of place value to tenths and hundredths and use the conventions of decimal notation to name and represent decimals.
• Number — apply place value understanding to communicate what digits represent in both whole numbers and decimals.
• Mathematical reasoning — use representations (materials/diagrams) to explain thinking about place value relationships.

Lesson structure (60 minutes)

1. 0–6 min · Hook (What does the digit mean?). Teacher shows a place value chart and writes the number 3,245, asking: “Where does the 2 sit? What might it represent?” Students point to the chart and give a quick verbal guess, then justify with one sentence using place value terms.

2. 6–18 min · Direct teach: four-digit place value. Teacher models 3,245 with base-ten materials (thousands, hundreds, tens, ones) and records the value of each digit on the chart. Students build the same number with manipulatives, then complete a “digit-position meaning” explanation for two digits (e.g., the 3 and the 4).

3. 18–28 min · Turn and talk with a model (guided). Teacher swaps one component (e.g., changes 3,245 to 3,275) using the manipulatives and asks: “What changed? What stayed the same?” Students respond by identifying the digit that changed and stating how the value changed using place value language.

4. 28–40 min · Bridge to decimals: tenths and hundredths. Teacher introduces a bar model divided into 10 equal parts labelled tenths, and then shows each tenth cut into 10 smaller parts to create hundredths. Students practise with a model: teacher shows 0.6 first, then 0.34, and students colour the matching parts while counting and naming (e.g., “three tenths and four hundredths”).

5. 40–50 min · Rename and justify (visual to notation). Teacher displays a model showing 0.25 and asks: “How do we write this using decimal notation?” Students write 0.25 in their workbooks, then explain which digit is the tenths place and which digit is the hundredths place. Teacher checks understanding by asking students to swap representations: “Model it again to prove your writing.”

6. 50–56 min · Independent/targeted practice (one-on-one check). Teacher gives 2 short tasks (on separate slips):

• Task A: Match a model to the correct decimal notation (two options).
• Task B: Write a decimal shown by a teacher-held model to two decimal places. Students complete both tasks while teacher observes and records any misconceptions (e.g., confusing tenths and hundredths).

7. 56–60 min · Exit ticket (quick assessment). Students answer one prompt: “Show and write 0.7 (tenths) and 0.72 (hundredths). Name them.” Teacher collects responses and notes accuracy of notation and naming.

Resources

• Place value chart (thousands, hundreds, tens, ones; tenths, hundredths columns)
• Base-ten blocks or place value materials (thousands/hundreds/tens/ones)
• Ten-strip bar model and cut-up parts for hundredths
• Coloured counters or sticky notes for tenths/hundredths shading
• Whiteboard or digital screen for teacher modelling
• Student workbook or paper, pencil and eraser
• Decimal notation cards (0.1, 0.25, 0.7, 0.72, etc.)
• Exit ticket slip with one question
• Visual number line with marked tenths (optional)

Assessment

• Formative: teacher checks during modelling (can the student build 4-digit numbers correctly and explain at least two digits?).
• Formative: observe student colouring/model-making for tenths and hundredths, and listen for correct naming (e.g., “three tenths and four hundredths”).
• Exit ticket: assess correct standard decimal notation to two decimal places and correct identification of tenths vs hundredths digits.

Differentiation

• Support: provide sentence starters such as “The 2 means … because it is in the … place” and “0.34 is … tenths and … hundredths.” Use fewer models at first (one decimal at a time).
• Support: pre-teach or remind that the tenths place is the first digit after the decimal point and the hundredths place is the second.
• Extension: offer an extra model (e.g., 0.58) and ask the student to explain a renaming relationship (for example, how one tenth equals ten hundredths) using the model.
• EAL/SEN: use consistent gestures for “after the decimal” and “two places after” and allow verbal responses instead of written explanations if needed, while still requiring correct notation.