# Analyse and respond (20 items)

After running the Check with students, use the following guidance to respond to the data gathered from the Number Check results. This guidance includes suggested follow-up activities and resources for each question in the Number Check.

## Classroom analysis and learning design

The results from the Number Check provide a starting point to evaluate students’ current level of number understanding. When combined with other observation and assessment evidence, teachers will gain a more complete picture of their students’ learning needs.

Analysing student errors allows teachers to see students’ specific strengths and weaknesses in number learning and gives teachers a means for selecting their teaching strategies. Similarly, examining student strategies in arriving at a correct answer may provide an insight into students’ level of understanding. For example, in Q3 of the Number Check, students who rely on counting each dot individually to get the correct answer may have a different level of understanding to those who are able to identify the number of dots by subitising a small group and counting on.

Teachers should carefully analyse students’ responses to the Number Check and other assessments to investigate the skills and knowledge students display to plan for differentiation. Such teaching is designed to accommodate students with different levels of number and counting knowledge and skills by differentiating at the point of practice and independent work. Differentiation strategies will sometimes involve the whole class and sometimes small groups or individuals.

After the Number Check, teachers may wish to follow up with relevant activities to develop knowledge and skills associated with each question that the student found challenging.

## Follow-up learning

To begin with, some students may benefit from activities that help them to recognise that a collection of objects can be made up of different arrangements. For example, seven stickers can be arranged as ‘a 4 and a 3’ in a tens frame layout which may minimise the need to count. Having students compose and recompose different arrangements and representations of different collections helps them to develop mental strategies.

Students need to develop their knowledge of place value, recognising that 10 is a building block of our numeration system. Tens frames are used to illustrate numbers less than or equal to 10, and are useful devices for developing number sense within the context of 10. By creating various arrangements of counters on the tens frames and posing simple questions, teachers can prompt students to use different mental images of numbers and different mental strategies for manipulating these numbers.

For suggested follow-up activities and resources for each question in the Number Check refer to the resources below or download this PDF.

### Video or interactive activity

Counting beetles
Select Level 1. Connect numerals and quantities. Students count the beetles on screen then select the correct number.

### Hands-on activities

• Have students trace with their finger the number to experience the numeral formation. Say the number name with the numeral representation.
• Have number cards, 1 to 10, and ask students to identify the number 6 card, as the numeral name is spoken.

### Video or interactive activity

Quantifying collections - paddlepop sticks 1

A video for students that explores regrouping and renaming when counting up to 20. Uses counting sticks to demontrate the pattern of regrouping and renaming a counted collection at each ten when counting forwards. Models ungrouping and renaming when counting backwards.

### Hands-on activities

• Have students identify the numerals of 12. Ask ‘What does the 2 represent?’ ‘What does the 1 represent?’ Draw on students’ understanding of place value.
• Model teen numbers using materials such as bundling sticks to demonstrate 1 ten and the ones (units).

### Video or interactive activity

Subitising: match my collection

View the video Subitising: match my collection

### Hands-on activities

• Using pasta or another uniform item, have students re-create the pattern of dots that are shown briefly.
• Have students draw the dots they see into a row or familiar array to assist with counting.

### Video or interactive activity

Number trains

Numbers 1–20 (Select Level 2)

In this activity, students place number carriages on a track in correct order, counting by ones to complete trains with carriages. It requires some problem-solving strategies to complete the task.

### Hands-on activities

• Use number cards, a string line and pegs, have students order the number cards in correct ascending order.
• Have students identify and place the ‘next card’ after a particular number card, such as 15, for numbers less than 20.

### Video or interactive activity

Number trains

Numbers 1–20 (Select Level 2)

In this activity, students place number carriages on a track in correct order, counting by ones to complete trains with carriages. It requires some problem-solving strategies to complete the task.

### Hands-on activities

• Use number cards, rope and pegs, have students order number cards in correct ascending order. Focus the ordering around the tens numbers, e.g. 9, 10, 11 or 19, 20, 21.
• Have students identify and place the ‘next card’ after a particular number card, such as 20, for numbers less than 30.

### Video or interactive activity

100 Square Jigsaw

Use the interactive 100 Square Jigsaw, which requires students to apply their understanding of counting both forwards and backwards to help them complete the square filled with numbers in the correct sequence. This activity draws on the student’s knowledge of what number comes before a particular number (from 1-100).

### Hands-on activities

• Use a hundreds chart and cover numbers with sticky notes. Have students identify the number that comes before (or after).
• Place a group of number cards in order e.g. 42, 43, 44, 45, 46, 47 and flip them over. Have the student identify the number before (or after) as cards are individually flipped over.

### Video or interactive activity

Number Chart
Use this interactive to compare and order numbers using a hundreds chart. Compare and order numbers with a large difference (for example, 12 and 21) as well as numbers with a small difference (for example, 40 and 41).

### Hands-on activities

• Provide regular opportunities for oral counting.
• Use manipulatives (such as Unifix, tens frames and counters, bead strings) to represent small sets of 2-digit numbers. Start by comparing and ordering two numbers. Then progress to three.
• Provide regular opportunities to interact with numbers on a number line.

### Video or interactive activity

Number trains

Numbers 30–50 (Select Level 3)

In this activity, students place number carriages on a track in correct order, counting by ones to complete trains with carriages. It requires some problem-solving strategies to complete the task.

### Hands-on activities

• Use base ten blocks to explore tens and ones (units) in counting patterns, and what happens when a number such as 49 is reached.
• Provide students with a large collection of items such as 56 icy pole sticks. Have students organise and count the objects. Then ask what is the total if I have one more object? Encourage students to count on.

### Video or interactive activity

100 Square Jigsaw

Use the interactive 100 Square Jigsaw, which requires students to apply their understanding of counting both forwards and backwards to help them complete the square filled with numbers in the correct sequence.

### Hands-on activities

• Have students create large number lines using masking tape and number cards. Have students stand on a starting number. Then ask what number comes before. Have the student move to the number. Continue to ask what number comes before establishing the number sequence.
• Provide students with a set of number cards mixed up and have them order the cards in sequence counting backwards, counting by ones.

### Video or interactive activity

Counting with understanding up to 100

Use this video to review the number naming sequence when counting by tens using concrete materials and tens frames.

### Hands-on activities

• Use the daily 100 days of school routine as an opportunity for oral counting by tens. For example, count the number of days attended in tens and ones, and count the number of days left until the 100 day target in tens and ones.
• Provide frequent opportunities for students to locate the mistake in a number sequence that counts forwards by tens (for example, 10, 20, 30, 40, 15, 60). Invite students to reason why this is incorrect and why it might be tricky.

### Video or interactive activity

Counting game (by multiples of 10)

Use this video to launch a hands-on, partner game where the goal is to get to zero by counting backwards by tens from 110.

### Hands-on activities

• Provide students with a 1–120 number chart and clear counters to place over each multiple of ten. Invite them to count backwards by ones starting at 120 but have them touch the counters and say out loud any multiples of ten and whisper all other numbers
• Provide frequent opportunities for students to locate the mistake in a number sequence that counts backwards by tens (for example, 120, 110, 90, 80, 70). Invite students to reason why this is incorrect.

### Video or interactive activity

Investigate ten-frames

Introduce ten frames for students to count and represent numbers 1 to 10.

Ten-frame filler

View the video to see how to play a strategy game to fill as many 10 Frames as you can. The game is played with a dice and a sheet with ten frames. A player who completes the ten-frame (for example, rolling a three and there is a ten-frame with 7 already filled), claims it by writing their initials on top of the ten-frame. The player with the most ten-frames at the end is the winner!

### Hands-on activities

• Provide students with 10 small objects such as counters. Have students collect a certain number of counters.
• Provide students with a tens frame. Have them populate the template with a set number of small objects/counters.

### Video or interactive activity

Dot card talk 1

In this video, students complete simple addition to 10 using dot cards (cards representing a number using dots). They are asked how they worked out the number.

### Hands-on activities

• Have two piles of small objects/counters e.g. 2 and 3. Have students count each pile of counters and then the total number of counters to find the total. Then have students practise counting on, by counting one pile (3) and then continue counting the rest of the counters to find the total.
• Provide two numbers (under 5). Have students draw the matching number of objects for each number and then count to find the total.

### Video or interactive activity

Dot card talk 4

In this video, students use tens frames to count collections of dots. They use strategies, such as adding dots from one frame to another, to make one full tens frame and one that is not full; making counting easier.

### Hands-on activities

• Have two piles of small objects/counters one with 9 and with a number less than 5. Have students use a strategy to find the total number of objects. Point out the bridging of the ten.
• Have students use tens frames to add numbers.

### Teaching sequence

Addition and Subtraction - Block 2

Introduce the language of subtraction, ‘Taking away’ in a range of real life contexts. Refer to the section, How many left? (pages 24-27)

### Hands-on activities

• Provide students with 15 small objects/counters. Have students practise taking away 5, 6, 7 and 8 from the group
• Draw chalk number lines on the ground to 20. Provide students with a starting number above 10, then have them subtract a provided number e.g. 5. Invite students to explain their thinking as they move along the number line to solve the problem.

### Video or interactive activity

Introducing rekenreks

Use this video to help students become familiar with rekenreks and explore them to consider numbers and number combinations to 10.

10 or bust game

Use this video to make observations about combinations to make 10.

### Hands-on activities

• Run regular number talks which involve a bridging 10 strategy. Start with very visual prompts (for example, 6 dots on a tens frame and 4 dots outside the tens frame). Invite students to work out how many and share their strategy.
• Use the activities in Addition and subtraction (within 10) to develop understanding, fluency and confidence with numbers to 10.
• Use Lesson 1 in this Addition: partitioning sequence. Provide students with 10 two-colour counters and use the context of red and green apples to explore different combinations to ten.

### Video or interactive activity

Compare and contrast? 3 Items

Use this Unifix visual to invite thinking about how the representations are the same as each other and how they are different. Highlight ideas that emerge about equivalence, part-part-whole understanding, and renaming.

Pose the questions:

• How else could this number be represented in two parts?
• How many different ways do you think there are?
• How might we know when we have them all?

How else could this number be represented in three parts?

### Video or interactive activity

Splat

Use this video to practise thinking about number problems where the difference is unknown. Invite different strategies to calculate how many dots are covered. Use similar examples that use larger numbers, for example, start with 11 dots, then cover 4 to leave 7 visible. How many dots are covered?

### Hands-on activities

• Provide frequent opportunities to explore and share strategies for additive story problems using concrete materials. For example, there are 12 ducks and we need to put them away for the night. We can only find 5. How many are missing?

### Video or interactive activity

Counting with understanding up to 100

Use this video to review the number naming sequence when counting by tens using concrete materials and tens frames.

### Hands-on activities

• Use  the Counting Collections routine to explore and count collections in different ways. Engage students in ongoing reflection about which strategies make sense and notice how their preferred strategies change over time with repeated practice.

### Video or interactive activity

Groups interactive 1

Use this interactive visual to students if they can work out (without counting by ones) if there are more orange dots or more blue dots. Invite students to share how they know. Highlight ideas that emerge about subitising, equivalence and part-part-whole understanding.

Groups interactive 2

Display this interactive visual and ask students to see if they can figure out (without counting by ones) if there are more orange dots or more blue dots. Invite students to share how they know.

### Hands-on activities

• Use the Counting Collections routine to explore collections of 10 items through to 20 items in different ways. Challenge students to find all possible ways to organise the number into equal groups. Invite them to consider: Is it possible with all numbers from 10 to 20? How do you know? How will you know when you have found all possible ways for your number?