Sanchita Dalal, a primary teacher at Kunskapsskolan Gurgaon in Gurugram (India), contacted Inquiry Maths to request more prompts for grades 1 to 3. 

In particular, she wanted ideas for topics that were coming up in the curriculum. The prompt on this page is the fourth of a sequence of five designed for the topics of number sense and addition and subtraction (see below).

Question, notice, wonder

The following questions and statements can help teachers guide novice inquirers.

Questions: Is the equation true? How do we know the two sides are equal?

Notice: The digits are consecutive. The digits are switched round.

Wonder: Would the two sides be equal if the digits are non-consecutive? Would they be equal if we changed the position of the digits (for example, 14 + 32 = 41 + 23)?

Teacher's aim

In the inquiry the teacher's aim is to encourage pupils to create their own examples with consecutive and non-consecutive digits and show their equations are true or not. 

In the initial stage the teacher should ensure pupils can find the sum of two two-digit numbers - perhaps by using an appropriate representation (see 'Lines of inquiry' below). She might also create examples to structure a period of whole-class exploration.

Intrigue

The addition prompt is intriguing with lots to discover. If you reverse the digits in the two two-digit numbers and the digits are consecutive, the two sides of the equation are equal if the largest and smallest digits are in the same column - that is, both tens or both units. For example, 65 + 34 works because the six (largest) and three (smallest) are both in the tens column.

However, non-consecutive digits will not always work if you follow the rule. For example, 97 + 14 does not work, but 97 + 13 does. 

Pupils might be able to generalise from a set of examples to find a rule that applies to all sets of four digits. If the two numbers on the left-hand side are 10a + b and 10c + d, the relationship between the digits has to be a + c = b + d. For example, in 74 + 25, a  7, b = 4, c = 2, d = 5, and 7 + 2 = 4 + 5.

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Sanchita would love to connect with teachers who use the prompt or other prompts from the sequence. Send feedback on your classroom inquiry to Contact Inquiry Maths.

July 2024

Question

• What does the arrow symbol mean?

Notice

• The digits are switched round in the numbers.

• In the first diagram, the bars represent tens and the squares represent units.

• The diagrams and numbers show the same inequality.

Wonder

• Does the inequality always work when you switch the digits?

• Is there another type of diagram to represent the inequality?

Teachers' notes

The prompt contains more information than a normal Inquiry Maths prompt. The teacher might choose to use only one representation at a time and support its use with concrete resources, such as counters or base ten tiles (pictured). Pupils could be invited to compare the four representations, giving advantages and disadvantages for each one.

The main activity might see pupils represent their own inequalities (or ones that the teacher gives them) in the four ways.

The inequality does not always work when you switch the digits. When the larger digit is in the tens column of the first number, the inequality sign should be reversed - for example, 74 > 47.

Question

• Is the equation true?

• How do we know the two sides are equal?

Notice

• The numbers are all even.

• The digits in the tens place have been switched round.

Wonder

• Would it always work if you switch the tens?

• What would happen if we switch the digits in the units place?

• Can we use all odd digits or a combination of odd and even?

Teachers' notes

The teacher's aim is to encourage pupils to create their own examples with digits that are either even, odd, or odd and even. In the initial stage of the inquiry the teacher would ensure pupils can add the two numbers on either side of the equation (using diagrams and number lines as appropriate). She might also create some examples to test if switching the tens always works.

Pupils should be aware (or the teacher should make them aware) of the properties of the examples they generate. By thinking about and defining the type of digits they use (odd, even, or both), pupils learn to test particular cases and, more broadly, to regulate their mathematical activity.