High Yield Routines
Overview
Strategies for Math
Introduction
Today, we will be exploring strategies from McCoy, Barnett, and Combs (2013) High Yield Routines, Grades K-8.
Guess My Rule
The Routine: A set of number pairs or an operational rule is presented to students. Students analyze the number pairs to determine the “rule” or relationship between the numbers, or students consider the rule and determine pairs of “in” and “out” numbers that demonstrate it.
Extensions: Students can apply a rule to a given set of “input” numbers or undo the rule given “output” numbers to find the input numbers. Students can create their own rule or set of number pairs and have a classmate determine number pairs or the relationship between the numbers. The teacher can specify what types of operations and numbers can be used. Multistep rules could also be used as a challenge.
Mathematical Content and Competencies: •
- demonstration of number sense, what numbers mean
- relationships between numbers
- looking for generalizations, functional relationships
- algebraic thinking
- flexibility and fluency with numbers
- operational skills and concepts
- representing quantity
- use of models
- apply mental math strategies
- communicate mathematical ideas
- connect mathematical concepts to each other and to the world
Alike and Different
Compare and Contrast Processes, Number, Fractions, Percentages, etc.
The Routine: A set of two or more objects (numbers, shapes, etc.) is presented to students. Students consider, discuss and share the similarities and differences between the objects.
Extensions: Place restrictions on how students need to represent the similarities and differences (a Venn diagram or other graphic organizer, using images, etc.), the number of similarities or differences that must be found, or the terms that must be used to describe the ways the objects are alike and different.
Mathematical Content and Competencies:
- comparative thinking
- demonstration of number sense, what numbers mean
- flexibility and fluency with numbers
- finding relationships among mathematical objects and concepts
- use of models • communicate mathematical ideas
- connect mathematical concepts to each other and to the world
- reasoning, critical thinking and problem-solving skills
- constructing logical arguments
How Do You Know?
The Routine: An open-ended question is presented to students. Students think about the question and discuss their responses with a classmate or small group. Students must explain and defend their answers.
Extensions: Teachers can have questions of a variety of levels to differentiate the activity for different students throughout the classroom. Teachers can specify what must be used in a response, for example, key terms, diagrams, operations, etc. Teachers can have students write an answer for a specific audience. Students can write their own questions for each other.
Mathematical Content and Competencies: •
- communicate mathematical ideas
- connect mathematical concepts to each other and to the world
- reasoning, explaining and building a strong answer
- introduction to conjecture and proof
- demonstration of number sense, what numbers mean
- flexibility and fluency with numbers
- use of models
- apply mental math strategies
Number Lines
The Routine: A number line that is strategically marked with values is presented to students. Students are asked to locate a value on the number line or determine the value of a marked location on the number line. Students explain or show their thinking (how they know that is the location of the value or that it is the value of the marked position). Students can explain themselves in words or by annotating the number line.
Extensions: The number of values to be determined can be changed depending on the level of the students. The number line can have fewer marked values, have different ranges of values (positive, negative, fractional, etc.). This routine can also be used for rounding.
Mathematical Content and Competencies:
- demonstration of number sense, what numbers mean
- flexibility and fluency with numbers
- composition and decomposition of numbers
- parts-whole relationships
- place value concepts
- representing quantity and magnitude
- use of models
- apply mental math strategies
- develop algebraic thinking
- communicate mathematical ideas
- reasoning, critical thinking and problem-solving skills
- constructing logical arguments
Quick Images
The Routine: An image is presented to the students for a short period of time (two-three seconds). This image can include a display of dots, geometric figures, base-ten blocks, or other materials. Students recreate what they saw by building, drawing or describing it. Students explain their own view of the image or model, including how they saw it or what it reminded them of.
Extensions: The teacher can change for how long the image is shown, how many times it is shown and the difficulty of the image. Students also enjoy creating images or constructions for their classmates to represent.
Mathematical Content and Competencies:
- composition and decomposition of numbers
- parts-whole relationships
- representing quantity
- use of models
- visual-spatial relationships
- positionality and transformational geometry
- apply spatial strategies such as subitizing
- communicate mathematical ideas
- connect mathematical concepts to each other and to the world
Mystery Number
The Routine: A set of clues is presented to students for a strategically chosen “mystery number.” Students discuss what each clue tells them about the mystery number, what some possible numbers may be, and what numbers it cannot be. Students use the clues to solve the mystery.
Extensions: Students can think of their own mystery number and create a set of clues for it. The teacher can set requirements for the clues. For example, the teacher can specify the type of mystery number, the number of clues, and the terms or operations that need to be used in the clues. Students solve each others’ mystery numbers.
Mathematical Content and Competencies:
- demonstration of number sense, what numbers mean
- flexibility and fluency with numbers • composition and decomposition of numbers
- parts-whole relationships
- place value concepts
- operational skills and concepts
- apply mental math strategies
- communicate mathematical ideas
- connect mathematical concepts to each other and to the world
- reasoning, critical thinking and problem-solving skills
- constructing logical arguments
Today's Number
The Routine: An intentionally selected “number of the day” is presented to students. Students create a variety of representations for the number. Students share and discuss their representations.
Extensions: Instead of being given a number, students think of their own number individually, in pairs, in small groups, or as a larger group. Students work with their own number or trade numbers with another person or group and create, share and discuss representations of it. Add enabling constraints depending on focus at the time.
Mathematical Content and Competencies:
- demonstration of number sense, what numbers mean
- flexibility and fluency with numbers
- composition and decomposition of numbers
- parts-whole relationships
- place value concepts
- operational skills and concepts
- equivalent expressions
- representing quantity
- use of models
- apply mental math strategies
- communicate mathematical ideas
- connect mathematical concepts to each other and to the world
Reflection
Complete this Google Form as a reflection of today's learning. Please reach out to one of the instructional coaches if you would like one of them to model the routines in your classroom, want to brainstorm any ideas, or want assistance in monitoring student progress.