How to Tier Math Lessons
by Luzviminda “Luchie” B. Canlas
Do you believe that all our students have the capacity to do well at learning mathematics? Do you think it is possible to reach and help all of them so they become confident in their abilities to understand mathematical concepts and principles?
We can do several things to achieve this. First, we must help build a community of learners in the classroom. Let’s help students to realize their strengths and discover areas that need improvement. Make them appreciate the fact that this diversity is a strength. Set up activities where they get to work together to see how they can depend on each other. Second, we must recognize that not all students learn the same way. Third, we must acknowledge the fact that we need to improve our instruction by intentionally planning to differentiate it to meet students’ varied needs. Then we should effectively assess where our students are: what they know; what they can do; what their interests are; and how they learn best, so that we can gather enough evidence to support them. We need to be creative, purposeful, and thoughtful enough to vary the ways we teach a lesson so that our visual, auditory, tactile, and kinesthetic learners are all supported. We should plan for coherent activities where we make students work in pairs, triads, quads, and other small groups. The questions we frame and pose should be open enough to promote rigorous math discourse and communication. We should give multiple opportunities for them to argue, provide reasons and proofs mathematically. Moreover, we must carefully craft developmentally appropriate tasks where we give our students instructional choices so that they can begin to own their learning. This way, they will be able to make meaningful connections and demonstrate their understanding in a deeper level. This will eventually lead toward achieving classroom equity.
What can we do to make this happen? Our students come to us with a wide range of readiness. They come in with a broad spectrum of abilities in mathematics. One way to differentiate instruction for them is to tier our lessons. What does it mean to tier a lesson? How is this done? Consider this example:
Examine this Multiplication Chart. Use this chart to complete your task.
x 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
1 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
2 
2 
4 
6 
8 
10 
12 
14 
16 
18 
20 
3 
3 
6 
9 
12 
15 
18 
21 
24 
27 
30 
4 
4 
8 
12 
16 
20 
24 
28 
32 
36 
40 
5 
5 
10 
15 
20 
25 
30 
35 
40 
45 
50 
6 
6 
12 
18 
24 
30 
36 
42 
48 
54 
60 
7 
7 
14 
21 
28 
35 
42 
49 
56 
63 
70 
8 
8 
16 
24 
32 
40 
48 
56 
64 
72 
80 
9 
9 
18 
27 
36 
45 
54 
63 
72 
81 
90 
10 
10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
Tier 1:
 List the multiples of 3.
 List the multiples of 6.
 Find the common multiples of 3 and 6 in this multiplication table.
 Find all the factors of 24.
 Find all the factors of 36.
 What is the Greatest Common Factor of 24 and 36?
Tier 2:
 List the common multiples of 4 and 6 in this table.
 Find 5 more multiples of 4 by extending this table.
 Find 5 more multiples of 6 by extending this table.
 Find all the factors of 72.
 Find all the factors of 24.
 What is the Greatest Common Factor of 72 and 24?
Tier 3:
 Find 5 more multiples of 8 by extending this table.
 Find 5 more multiples of 9 by extending this table.
 2. List the common multiples of 3, 4, and 6.
 Find the Greatest Common Factor of 12, 48, and 72.
 What conclusions can you make about the number of multiples a number can have? Explain your answer.
 What conclusions can you make about the number of factors a number can have? Explain your answer.
In this example, notice that all your students will be using the same Multiplication Chart but will answer different sets of questions based on their readiness. When tiering a lesson, we are to teach one concept, standard, or big idea and then design activities that will allow children to express their own understanding based on their different readiness levels, interests, or learning profile. In this particular example, the big idea being taught is that: by classifying numbers and knowing their relationships, conclusions can be drawn about them. To teach this, the questions were varied according to their different readiness levels. The first tier is for the lower leveled learners, the second tier is for the grade level learners, and the third tier is for the higher leveled learners. Take note that the questions were framed to challenge the students appropriately. They were adjusted so that the questions are at different levels of difficulty. When making these questions and assigning students to tiers, make sure that you know your students very well. Make sure that you ask questions that children can answer confidently. It is essential that they experience success and develop confidence when performing these tasks.
Here are some steps to follow when tiering a lesson:
 Read the math state standard and understand the key performance indicators (what each student is expected to do).
 Understand well the key concept or standard you are to tier.
 Assess you students. Find out what their needs are.
 Decide on what you want to tier (content, process, product) and type of tiering you will do (Will it be based on their interests, readiness levels, or learning profile?).
 Form your groups. Decide on the number of tiers you will have.
 Create your tiered lesson activities.
 Assess your students.
 Plan to reteach for those who didn’t get the lesson.
The number of tiers you use will vary depending on the number of groups of students you have. Sometimes, you will have more than three tiers or less than three. The size of your groups will not be the same. When tiering, you are not planning to have groups of equal size. You are planning to have flexible and dynamic groups with similar needs that will perform a task that will challenge them appropriately to reach their full potential in mathematics.
Finally, in an academically diverse math classroom, it is imperative that we invest enough time, energy, care, thought, and patience in developing and planning differentiated tiered lessons. We need to start soon, but carefully so that we can help our all students achieve the success they so deserve.
If you have a question or comment about this article email Luchie.
