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# Limited understanding of tens and ones in numbers to 100

### Diagnostic questions

1. Ask the student to count from:
a. 12 to 23      b. 27 to 35      c. 66 to 72
2. Ask the student to count back from:
a. 9 to 2      b. 24 to 16      c. 62 to 55

### What to notice in the student’s response

• Does the student mix up decades, for example, counting 12, … 18, 19, 40, 41, 42 or similar?
• Does the student stop counting when they reach a new decade?
• Does the student struggle when counting back?
• Can the student only count backwards from 10?

### Deliberate acts of teaching

#### Materials

These activities help the student to increase the fluency with which they count on or back from a number.

Connecting the digits 0–9 with larger numbers: Ensure that the student is secure with counting up and back from 0–9. Write the digits 0–9 in a line or as a column. Count on from a number larger than 20, pointing to the appropriate digits in the line or column. For example, if counting on from 24, start by pointing to the 4, then for 25 point to the 5, for 29 point to the 9, for 30 point to the 0, for 31 point to the 1. Repeat the process counting back (Refer to the Oamaru North School: ALiM report).

Number line to hundreds board: The student may not realise that a hundreds board is simply another way of presenting a number line. Create a set of numbers in decades with magnetic strips on the back, for example, 1–10, 21–30, 51–60. Ask a group of students to stand in a line, holding the decades in the right order, to create a number line. Ask the students to put the numbers on a magnetic board, placing each decade above a smaller decade.

Counting: Relate the number counted-on to fingers, for example, if counting on five from 17, ask the student what the next counting number after 17 is. As the student says 18, they hold up one finger (keeping it up), at 19 they hold up two fingers (keeping both up), continuing until they have reached 22 and are holding up five fingers. Keep using 5 as the number to add on so that the student only needs to use one hand. Use the same approach to help the student to count backwards, ensuring that the student knows that for addition they count on from the next number, but for subtraction they have to start with the number that comes before the starting number.

Feeding the chickens: Give the student practice in subtracting numbers, for example, 9 – 4. Place nine beans in a circle and ask the student to remove four beans, one bean at a time, counting down as they do so, for example, “9”, (remove one) “8”, (remove one) “7”, and so on. When the student has removed four beans and the count has reached “5”, they will see that there are five beans remaining. Give the children several similar problems to increase their confidence in counting back.

### What to do next if the student is stuck

Return to activities involving shielding one set, for example, Fly Flips (Material master 4-5) (PDF, 91KB).
Use fives frames to give the student practice with language such as less, more, before, after, even, odd, and closest. For example, “4 is one less than 5, 4 comes before 5, 4 is closer to 5 than 1, 4 is two more than 2, and 4 is an even number”.
Use 5 as a benchmark to add on from, building up the structure of 5 and one more, 5 and two more.

### Initiating home-based activities

Ask parents to give the student daily practice counting forwards and backwards from two-digit numbers.
Give parents the “Supporting your child’s learning” booklet for year 2 students (also available on www.tki.org.nz). Highlight useful activities.

### Next teaching steps back in the classroom

Work on counting in tens, for example, moving from 4 to 14 to 24, all the way up to 104 and back down to 4.
Ensure that subtraction work is given equal time with addition work. Counting backwards and comparing the size of numbers is important for the development of number sense.
Use addition and subtraction problems in contexts relevant to the student.
Use problems where the student is encouraged to start counting on or back from the larger of two numbers.