Foundations for meaningful math.
Primary Intervention
My approach to intervention at the Primary level is a series of building blocks. One skill should be firmly in place before moving on to the next skill. The following is the progression that I follow:
​
Conceptually subitizing to 10
Anchor Facts - One/Two More/Less
Anchor facts - Ways to make 5
Anchor facts - Ways to make 10
Conceptually subitizing to 20
Anchor facts - Doubles
Fact strategies - Using anchor facts to solve harder facts
Subtraction - Math Stories
Count and Write to 120
Adding groups of 10
Adding tens and ones
**Below is a description of each building block. Visit the "Intervention Resources" tab for easy to implement activities to support each building block.
Subitizing to 5
Student should be able to quickly and accurately recognize a quantity of items up to 5 without counting.
Conceptually subitizing to 10
The human brain can visually recognize quantities up to 5. After 5, subitizing becomes a conceptual task. A student may recognize a quantity 6, by seeing 5 and one more, or the quantity 9, by seeing one less than ten. Visually recognizing smaller quantities and combining them or taking away from them is what allows students to conceptually subitize. The benchmarks 5 and 10 are an important part of this process, but students may also make use of other groupings. For example, two groups of three makes six.
Anchor Facts - One/Two More/Less
Fact fluency is a pillar of Primary level math, and anchor facts are where fluency begins. (Visit the Philosophy page of my site to understand what fluency really means.) For Primary students, knowing what is one more, one less, two more, and two less than a given quantity is the beginning of fact fluency. The goal is for students to know automatically without having to count. Repeated experiences with the counting sequence and number paths allow this skill to become intuitive for students.
Anchor Facts - Ways to Make 5 and 10
Knowing automatically all of the different the quantities that combine to make 5 and 10 is also a vital building block leading to fact fluency. These combinations should not be memorized, rather, repeated exposure to concrete and visual experiences will lead to a conceptual understanding that will allow students to use these anchor facts with flexibility in solving related problems. For example, if a student know that 7 and 3 make 10 they can use that information to know that 7 and 4 would be one more than 10.
Conceptually Subitizing to 20
Students should be able to visually recognize quantities from 10 to 20 by recognizing a group of 10 and some more. This skill gives students a concrete understanding of teen numbers that leads to the flexibility to make 20 and use the same strategy to combie larger quantities by making the next ten.
Anchor Facts - Doubles
Concrete and visual experiences with doubles facts (and the related ten and some more facts) give students the flexibility to solve harder related facts. For example, if a student knows that 6 and 6 makes 12 then they can also understand that 6 and 7 is one more. A concrete understanding of doubles facts can also help students to solve problems with larger quantities like 40 + 40 as four groups of ten plus another 4 groups of ten.
Fact Strategies - Using Anchor Facts to Solve Harder Facts
The goal of fact fluency is not memorization, but rather, a deep conceptual understanding of known anchor facts through the use of concrete tools and math visuals. This deep understanding allows students to apply what they already know, with flexibility, to solve harder problems. For example, a student with flexibility might be able to solve the challenging fact 8 + 9 in many different ways. They may know the "doubles" fact 8 + 8 equals 16 and therefore 8 + 9 is one more. Or they may know the "way to make ten fact" 8 + 2 equals 10 so 8 + 9 is 7 more. Or they may know the "ten and some more" fact 8 + 10 equals 18 so 8 + 9 is one less. These same strategies can be applied to problems with larger quantities. For just one example, 28 + 39 can be simplified into 27 + 40. A full and complete understanding of anchor facts is the foundation to student fluency.
Subtraction - Math Stories
My first few years teaching 1st grade I really struggled with helping my students make the leap from addition to subtraction. Since that time I have discovered two things. When students know their addition facts and have flexibility with addition the transition to subtraction is usually very intuitive. There may be a few students that still struggle. I regularly follow the Build Math Minds blog, so when I got to a point that I didn;t know what to do to better support my students in transitioning to subtraction, I emailed Christina. Her suggestion was to use subtraction in the context for math stories to bridges students from addition to subtraction. For example, begin by asking a simple math story using a well know fact. Jill has 5 pieces of candy and Marco has 3 pieces of candy. How many do they have altogether? And then ask a related subtraction problem. If Jill has 8 piece of candy and give 3 to Marco then how many does she have left. I have found this to be a very effective strategy with all students except those with the greatest struggles with language.
Count and Write to 120
Counting and writing to 120 should be as much a concrete and visual activity as all of the other building blocks. Counting collections and beaded number lines are just a few of the resources I use to support my students in a conceptual understanding of our place value system that gives them a meaningful understanding that supports them in solving really hard problems.
Adding Groups of Tens and Adding Tens and Ones
At the 1st grade level, I support my students in developing these skills by presenting them with compelling productive struggle tasks or engaging games paired with carefully chosen math tools. The number sense that my students develop through the previously described building blocks combined with, engaging activities, and effective math tools allows them to make many meaningful connections about adding tens and ones and efficient strategies on their own.