Digital Resource 3.1: Dr. Burkhart’s Modeling Activity
Connected to the opening vignette, this modeling activity includes slides for establishing the context, making observations about the first grade data, and considering ways first graders might approach the situation. Also included in the activity is an opportunity to approximate the practice of analyzing student thinking, with three student work samples.
Digital Resource 3.2: Base Ten Numeration
Aligned with 3.4.1.3 Big idea: The base ten place value system of numerals relies on patterns and the position of the digits reveals the value, the Base Ten Numeration activity includes slides that present base ten pieces as part of a growing pattern with connected visual and numerical representations. This activity can also be extended as a pattern that continues in both directions allowing for the meaningful exploration of negative exponents.
METIII Elem 3.2_BaseTenNumeration
Digital Resource 3.3: Multidigit Subtraction Strategies
Aligned with 3.4.2.2. Big idea: Efficient computation methods rely on composing and decomposing numbers, strategically breaking the calculation into parts, the Multidigit Subtraction Strategies activity provides six different strategies for computing 62 – 27. Through representing the strategy verbally, visually, and contextually, there is an opportunity to consider the viability of each approach as well as ways the strategy takes advantage of the base ten system.
METIII Elem 3.3_MultidigitSubtractionStrategies
Digital Resource 3.4: Naming Fractions and Seeing Equivalence
Aligned with 3.4.3.2. Big idea: There are multiple strategies for comparing and determining equivalent fractions, the Naming Fractions and Seeing Equivalence activity uses an egg carton model to examine the varied fraction names evident in the model showing 8 “eggs” in a 12-egg carton. The activity naturally extends into completing an Egg Carton Wall chart and observing the patterns and rationale for their existence.
METIII Elem 3.4_NamingFractions&SeeingEquivalence
Digital Resource 3.5: Fraction Representations and Constructs
Aligned with 3.4.3.3. Big idea: Fraction constructs emerge from varied representations and are equivalent when modeled with the same size whole (referent unit), the Fraction Representations and Constructs activity extends the use of the egg carton model to investigate this equivalence and how the meaning of the numerator and denominator changes across constructs, later connecting to varied friendship bracelet story contexts that illustrate the constructs and a modeling with mathematics task.
METIII Elem 3.5_FractionRepresentations&Constructs
Digital Resource 3.6: Data Talk – Apple Taste Testing
Aligned with 3.4.4.1. Big idea: The statistical problem solving process involves questioning throughout each phase, the Apple Taste Testing graph and related data talk provide both a specific activity as well as a general structure for a discussion that invites observing, problem posing, predicting, sense making, justifying, and communicating.
Digital Resource 3.7: Sorting Data Cards
Aligned with 3.4.4.2. Big idea: There are multiple types of data and variables and situations can require reasoning with more than one variable at a time, the Sorting Data Cards activity provides an opportunity to explore a multivariate dataset by examining, organizing, and sorting physical or digital data cards. Each card represents an individual case and includes multiple categorical and numerical attributes. Create cards in person or generate a random sample of data cards using data from the U.S. Census at School (ASA, n.d.)
METIII Elem 3.7_SortingDataCards
Digital Resource 3.8: Two-Dimensional Shapes and Their Attributes
Aligned with 3.4.5.2. Big idea: Geometric objects are defined by their constituent parts and relationships among those parts, the Two-Dimensional Shapes and Their Attributes activity provides an opportunity to fold a circle and explore a series of two-dimensional shapes created by folds. Make observations, identify relationships and defining characteristics, and develop and test conjectures informally proving features of those shapes (e.g., congruence and symmetry).
METIII Elem 3.8_2DShapesAndTheirAttributes
Digital Resource 3.9: Choosing a Cake Pan
Aligned with 3.4.6.1. Big idea: Measurements of an object’s attributes are interrelated and imprecise, the Choosing a Cake Pan activity explores ways to compare Nordic Ware cake pans by identifying measurable attributes and using those attributes to evaluate the pans. Investigate the distinction and relationship between dimensions, base perimeter, surface area, and volume.
METIII Elem 3.9_ChoosingACakePan
Digital Resource 3.10: Investigating Areas of 2D Figures
Aligned with 3.4.6.2. Big idea: A range of equivalent area and volume formulas can be obtained by transforming figures with unknown areas or volumes into figures whose areas or volumes can be reasoned about using familiar figures, the Investigating Areas activity invites papercutting and folding to find general approaches for determining the area of 2D figures. A similar approach can be used for 3D figures using geoblocks and graph paper.
METIII Elem 3.10_InvestigatingAreasof2DFigures
Digital Resource 3.11: Odd and Even Number Pattern
Aligned with 3.4.7.2. Big idea: Thinking algebraically includes developing habits of noticing structure and repeated reasoning, the Odd and Even Number activity begins with noticing and wondering about a visual of odd numbers presented as a growing pattern. From the observations, varied ways of “seeing” the number of squares in each arrangement can be generalized to any arrangement with connections being made within and across visual, symbolic, and graphical representations. The process is then repeated with the even number visual pattern.
METIII Elem 3.11_Odd&EvenNumberPatterns
Digital Resource 3.12: Examples of Cross-Curricular Connections
A brainstormed list of the connections across the elementary curriculum (i.e., literacy, science and health, social studies, and social and emotional learning) between three modeling with mathematics tasks along with general connections to inquiry-oriented instructional approaches.
METIII Elem 3.12_CrossCurricularConnections
Digital Resource 3.13: Alignment of Activities with Developing Teachers as Doers, Knowers, and Sense Makers
A summary of the connections between the ready-to-use activities and the elements of the Cycle of Doing, Knowing, and Sense Making. Also included are additional activity connections to the elements of elementary teacher identity development and purposeful use of tools and technologies.
Digital Resource 5.0. Examining Students’ Understanding of Short-Term Exponential Behavior
A full version of the task discussed in the opening vignette from the high school chapter that is ready to use in your classroom!
Digital Resource 5.1. Working with Relations
A classroom-ready version of the task from Example 5.1 to support teachers in thinking about relations from a covariation perspective. The resource includes commentary on how the task can be used, sample solutions, and links to GeoGebra applets to dig into the mathematics.
Digital Resource 5.2. Reasoning from Covariation and Correspondence
A task that can be used to introduce the idea of covariation and correspondence perspectives on functions. This task builds on the scenario presented in Example 5.2. Commentary and sample solutions are provided.
Digital Resource 5.3. Connecting Error Bounds and Limit Theorems to the Concept of Square Root
A task that can be used in a real analysis course or other course addressing the foundations of calculus to make sense of error accumulation using a scenario from high school teaching. This resource provides a classroom-ready version of Example 5.3.
The Mathematical Education of Teachers III Supplemental References