Benchmark Families
Fact Families show us how a group of numbers relates to each other. A student’s family teaches us more about how best to teach the student. The idea of families and relationships holds true for each of the Minnesota benchmarks as well.
Think of a benchmark as a student who comes with their parent to conferences. After meeting a parent or another person in the family, we leave with a better understanding of the student and how to teach him or her. This is the same situation with the benchmarks. When we want to better understand and teach a benchmark, getting to know its family becomes essential.
Below are steps that you can follow to “meet” the benchmark family for 5.1.1.1. (At the end of the steps is a PDF with a visual of the family.)
5.1.1.1 Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal.
- Meet the parents: Look at the grade below the benchmark. For benchmark 5.1.1.1, look at grade 4 for benchmarks that lead to 5.1.1.1. For example, see benchmark 4.1.1.6. (Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction.)
Other grade 4 benchmarks also relate to 5.1.1.1. Determine if they are parents or uncles and aunts of the benchmark. Here is a list to consider 4.1.1.1, 4.1.1.3, 4.1.1.4, 4.1.1.6, 4.2.2.1, 4.2.2.2.
- Meet the siblings: Look at the same grade to see where the benchmark falls within the grade. For benchmark 5.1.1.1, look at grade 5 benchmarks that have similarities and/or overlapping concepts. For example, see benchmark 5.1.1.4. (Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.)
Other grade 5 benchmarks also relate to 5.1.1.1. Determine if they are siblings or cousins of the benchmark. Here is a list to consider 5.1.1.2, 5.1.1.3, 5.1.1.4, 5.1.2.4.
- Meet the children: Unlike most students in K–12, benchmarks have children. Look at the grade above the benchmark. For benchmark 5.1.1.1, look at grade 6 for benchmarks that build on 5.1.1.1. For example, see benchmark 6.1.3.1. (Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms.)
Other grade 6 benchmarks also relate to 5.1.1.1. Determine if they are children or nieces and nephews of the benchmark. Here is a list to consider 6.1.2.1, 3.1.3.2, 6.1.2.4
- Meet the rest of the family: Look further from the benchmark, two or even three grades in each direction. For 5.1.1.1, consider the following benchmarks as possible grandparents: 2.1.2.1, 3.1.2.3, 3.1.2.4, 3.1.2.5, 3.2.2.2. Then consider the following benchmarks as possible grandchildren: 7.1.1.2, 7.1.2.1, 8.1.1.5.
Following these steps is one way to “get to know the family”. No matter what set of steps you use, building relationships with the benchmarks enhances our ability to teach the benchmarks to our students.
See a PDF visual of these relationships for benchmark 5.1.1.1.
As always, please do not hesitate to contact me with any questions, concerns, or requests to work with your school.
Angela Hochstetter