This collection of resources helps to guide students through the process of constructing viable arguments and critiquing the reasoning of others (CCSS Practice Standard 3). Students learn to use logical reasoning to solve problems and to explain their thinking, as well as to consider and reflect upon solutions offered by others. Initially teachers may need to model these practices but with experience, students eventually will be able to complete many of the activities independently. Additional resources for educators can be found in a companion Professional Development collection, "Incorporating CCSS Practice Standard 3."

ResourceTitle/DescriptionGrade Level

K, 1

This activity helps students become familiar with positional words and develop systematic thinking. Students use the clues provided to arrange six colored squares in an array, either on paper or with the interactive Flash applet that is provided. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support and a printable sheet (doc). Students may be asked to create a similar problem for others to solve.

K, 1, 2

This problem helps learners become more familiar with odd and even numbers and addition facts within five. By challenging them to justify their findings, it also develops reasoning and communication skills. The problem displays 9 dominoes and asks the student to sort them according to parity, and then into pairs totaling 5 pips. It poses questions that stimulate thinking about basic number concepts. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and a link to an interactive Dominoes Environment (cataloged separately).

K, 1, 2, 3

This activity helps students develop a sense of the relative size of quantities in time, length and mass. Learners rank their estimates of given measures in order from least to greatest and justify their decisions. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support, printable cards (pdf), and a link to a related problem, "In Order" (cataloged separately). The solutions page shows that students used standard units of measure to make their comparisons.

3, 4, 5

This Java applet allows children to explore a balancing tool and thus build their algebraic thinking about equivalency. By placing shapes on each side of the balance and finding equivalent sets of weights, students discover the weight of each shape in one of six built-in sets or a random set.

In this 3-part video series, second grade students hone their estimation skills in a graduated process that employs consensus building. In the course of a lesson involving cranberries, students make connections among number, measurement and data concepts. Video transcripts, comments and reflections for educators are included.

2, 3, 4, 5

This problem provides an opportunity for students to form and test conjectures, and make generalizations, while exploring the effect of parity on simple whole number sums. Solvers are asked to arrange given sets of numbers in a V formation so that the sums of the numbers in each "arm" are equal. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, a printable record sheet (pdf) and links to two YouTube videos demonstrating use of the problem in a professional development setting (videos cataloged separately).

3, 4, 5

This activity helps students develop a sense of the relative size of quantities in the categories of temperature, speed, time duration and loudness. Learners rank their estimates of given measures in order from least to greatest and justify their decisions. Students are encouraged to do research and carry out experiments when possible. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support, and links to related activities.

In this series of three lesson plans from PBS Mathline the instruction is focused on utilizing probability terms in everyday and mathematic situations. Each lesson plan is accompanied by an activity sheet, extension suggestions, and questions for professional development discourse. The video for Part 1 is cataloged separately and is listed as a related resource.

3, 4, 5

In this statistics lesson on bias sampling students conduct a poll of specific populations within their school to determine recommendations for homework policies. Each of three groups is assigned a population to survey and then reports their conclusions to the class. Students will then determine how to improve their survey in order to get unbiased results. A student worksheet for questions and a student template for a letter to the principal are included.

3, 4, 5

This problem provides a context in which pupils apply their knowledge of number properties and practice explaining their reasoning. Students decide which of the eight clues provided are necessary in order to determine a specific number on a 0-99 grid. The activity includes teacher notes, hints, sample solutions, a printable pdf of the problem, and a link to a more accessible related problem.

3, 4, 5

The activities in this Illumination lesson plan deal with patterns and the importance of looking at an object/item from more than a single perspective and reaffirms to learners that numerous reasonable solutions are possible. Students investigate a series of items (a list of class names and a parade of animals) that appear to be ordered in some "obvious" ways and also explore ways of sorting items ( a deck of cards and numbered horses) into two disjoint groups on the basis of some definable characteristic. Activity sheets are included in pdf format.

4, 5, 6+

These 5 activities, part of the Mathematics Developmental Continuum of the State of Victoria, Australia, are intended to introduce learners to making conjectures and using counterexamples in proofs. Investigations into the theory of numbers provide the content. Supporting documents, and progress indicators are included.

5, 6+

This data analysis activity requires students to read and interpret six written or graphical representations of data. Students must determine which graphs and analysis belong together. The data representations used include a pictograph, a circle graph, a frequency chart, a bar graph, and two written analyses including the terms mode, median, and mean for each data set. Included with the activity are teacher's notes, a hint, and the solution.