# Domino Trails

### Task 15 ... Years K - 6

#### Summary

A domino trail is provided on the white card. It is a 'C' shape of dominoes end to end which finish at a circle. A number is written in the circle.
• Can you make a domino trail so that the total of the domino dots is the number in the circle?
• A matching domino trail has the special rule that squares which touch must be the same number of dots. Can you make a matching domino trail to equal the number in the circle?

This cameo has a From The Classroom section showing teachers exploring floor dominoes in a workshop. Floor dominoes are linked below.

#### Materials

• Set of double-six dominoes
• Playing board, marker and cloth
• Recording sheet

#### Content

• 1:1 correspondence
• sorting
• number recognition
• counting
• multiplication and division
• problem solving strategies

#### Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

This task is very open-ended and experience suggests that most students love creating their own target and trying to make the dominoes add to it. Heaps of arithmetic practice in a problem-solving situation:

Had a great session with Domino Trails out at Amanbidgi. One teacher school, 15 Indigenous students from prep to grade six. We played dominoes, looked at the patterns of the dots, selected dominoes with a given value and then in pairs made up two, three, four and five domino trails. Kids were really good and two groups of girls made five sets of three domino trails that equal 12 from the one packet. Children worked for over an hour, wrote nothing down on paper but did lots and lots of sums. We even looked at the difference between some dot patterns.
Eric Smith
Clearly Eric and the kids have asked the mathematician's question What happens if ... we change the length of the trail? Implied too is the question What happens if ... we change the target number.

The card also suggests another level of reasoning. For a given length of trail, what is the maximum possible target and what it the minimum possible target. Maximum and minimum values are a favourite study of mathematicians. But when we find those answers for a given length of trail, there is still at least one more question. Is it possible to make trails which total to each and every possible total between the highest and lowest?

For a 3 domino trail it might even be possible to answer the question: In how many ways can each of these totals be made?

Of course, all the questions above could be asked separately for domino trails and matching domino trails.

#### Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.

The whole class lesson for this task is detailed in Maths300 Lesson 95, Domino Trails. However, you can expand this investigation by beginning with Floor Dominoes. This PDF file contains a full set of double six dominoes (28 pages) with one domino per landscape page. They can be used over and over if each domino is stored in a plastic envelope.

To continue the investigation it is best if you have enough sets of dominoes for one between two. However, the lesson does supply a printable set of dominoes and if these are printed onto card and laminated they work well; but they are a little more difficult for small fingers to pick up.

In addition, the lesson offers a wonderful set of extra task cards suitable for a range of ages. Most importantly though their presence suggests that students could contribute their own puzzle cards to a class set of domino problems.

For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 95, Domino Trails, which includes other task cards that extend the use of dominoes.

#### Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.

The Domino Trails task is an integral part of:

• MWA Number & Computation Years 3 & 4

The Domino Trails lesson is an integral part of:

• MWA Number & Computation Years 3 & 4
This task is also included in the Task Centre Kit for Aboriginal Students.

## From The Classroom

#### Working Like A Mathematician

C. E. O Canberra Goulburn
Teachers
Teachers were introduced to Floor Dominoes in this segment of a six day professional development program. It was the Day 5 and they had become used to working from an open starting point. There were enough teachers so that each person had their own floor domino to contribute to the group challenges.
Work together to arrange your dominoes on the floor.

 Arrange by matching, just like the dominoes game. They all have a place. Arranged by sequences.

 Okay, let's start with a number sequence in the bottom row - 0, 1, 2, ... Then we get this. Neat! That's like the Staircase tasks (#51 & #61).

 Or we could build a different staircase and... ...this is how we could find the number of dominoes without counting them all.

 Now we are familiar with the dominoes we can make trails. The target is 17 with 3 dominoes. We can do it another way. And we can do it with 5 dominoes. Could we do it with 3 or 5 dominoes that match like in the first pattern?