This problem uses the context of a growing plant in which to practice doubling and also to develop representation and recording strategies. The Teachers' Notes page offers suggestions for implementation and discussion as well as ideas for extension and support.
In this activity, students discuss the notion of time and how time can be measured. They learn that a long time ago, people used different tools to measure time. Students build and use a sundial and discover that a long time ago, it was much more difficult to accurately tell the time than it is today.
A realistic mass and spring laboratory. Hang masses from springs and adjust the spring stiffness and damping. You can even slow time. Transport the lab to different planets. A chart shows the kinetic, potential, and thermal energy for each spring.
A realistic mass and spring laboratory. Hang masses from springs and adjust the spring stiffness and damping. You can even slow time. Transport the lab to different planets. A chart shows the kinetic, potential, and thermal energy for each spring.
Math Teacher Dilemma: Standard 7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh grade science book are generally longer than the words in a chapter of a fourth grade science book.
This formative assessment exemplar was created by a team of Utah educators to be used as a resource in the classroom. It was reviewed for appropriateness by a Bias and Sensitivity/Special Education team and by state mathematics leaders. While no assessment is perfect, it is intended to be used as a formative tool that enables teachers to obtain evidence of student learning, identify assets and gaps in that learning, and adjust instruction for the two dimensions that are important for mathematical learning experiences (i.e., Standards for Mathematical Practice, Major Work of the Grade).
This brief article for young learners describes how ancient cultures developed units of measurement like the cubit and foot, and how estimation and precision play a role in measuring today. A printable page is available.
This is a computer science lesson plan created by educators in the South Sanpete School District. Using Sphero robots, students will program their Sphero to drive as close to an object as possible without touching it and change color when it stops. They will then measure the distance from the object to their Sphero. The lesson is designed for second grade and includes modifications for grades 1-5.
The main aim of this lesson is to show students that distances may be determined without a meter stick—a concept fundamental to such measurements in astronomy. It introduces students to the main concepts behind the first rung of what astronomers call the distance ladder. The four main learning objectives are the following: 1) Explore, in practice, a means of measuring distances without what we most often consider the “direct” means: a meter stick; 2) Understand the limits of a method through the exploration of uncertainties; 3) Understand in the particular method used, the relationship between baseline and the accuracy of the measurement; and 4) Understand the astronomical applications and implications of the method and its limits. Students should be able to use trigonometry and know the relation between trigonometric functions and the triangle. A knowledge of derivatives is also needed to obtain the expression for the uncertainty on the distance measured. Students will need cardboard cut into disks. The number of disks is essentially equal to half the students in the class. Two straight drink straws and one pin per disk. Students will also need a protractor. The lesson should not take more than 50 minutes to complete if the students have the mathematical ability mentioned above. This lesson is complimentary to the BLOSSOMS lesson, "The Parallax Activity." The two lessons could be used sequentially - this one being more advanced - or they could be used separately.
An article based on data and evidence that includes charts and information that can be analyzed statistically by students.
This problem, based on the story of Goldilocks and the Three Bears, provides a context for children to apply ratio and proportion concepts as well as fraction computation skills. Using the given size relationships among the bears, solvers determine the sizes of various objects in the bears' house. The Teachers' Notes page offers suggestions for implementation, key questions, ideas for extension and support, a printable pdf of the problem, and links to related problems.
Open Middle tasks provide opportunities for student to approach a mathematical task using different strategies and representations. They can be used as a warm-up/closing activity, as a formative assessment, or to facilitate discourse and discussion and get insite into student thinking and problem solving. These tasks provide a great opportunity for student to engage with the Standards for Mathematical Practice.
Open Middle tasks provide opportunities for student to approach a mathematical task using different strategies and representations. They can be used as a warm-up/closing activity, as a formative assessment, or to facilitate discourse and discussion and get insite into student thinking and problem solving. These tasks provide a great opportunity for student to engage with the Standards for Mathematical Practice.
Open Middle tasks provide opportunities for student to approach a mathematical task using different strategies and representations. They can be used as a warm-up/closing activity, as a formative assessment, or to facilitate discourse and discussion and get insite into student thinking and problem solving. These tasks provide a great opportunity for student to engage with the Standards for Mathematical Practice.
This problem provides an opportunity for students to reason about ratio and proportion in the realistic context of mixing a fruit drink from concentrate. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and links to related problems (Blackcurrantiest is cataloged separately).
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.
This interactive Flash animation allows students to explore size estimation in one, two and three dimensions. Multiple levels of difficulty allow for progressive skill improvement. In the simplest level, users estimate the number of small line segments that can fit into a larger line segment. Intermediate and advanced levels offer feature games that explore area of rectangles and circles, and volume of spheres and cubes. Related lesson plans and student guides are available for middle school and high school classroom instruction. Editor's Note: When the linear dimensions of an object change by some factor, its area and volume change disproportionately: area in proportion to the square of the factor and volume in proportion to its cube. This concept is the subject of entrenched misconception among many adults. This game-like simulation allows kids to use spatial reasoning, rather than formulas, to construct geometric sense of area and volume. This is part of a larger collection developed by the Physics Education Technology project (PhET).
This interactive applet reinforces students' knowledge of the properties of rectangles and gives them a game in which to form and test hypotheses. In a 5x5 grid in which a rectangle has been hidden, students try to fix the location with the fewest number of probes (Note: press 'Start' to hide a different rectangle). Ideas for implementation, extension and support are included along with printable sheets and video clips of classroom testing.
In this NRICH article the authors discuss the definition of problem solving and the three ways the topic can be considered in the classroom: teaching for problem solving, teaching about problem solving and teaching through problem solving. Using examples from the NRICH site, the authors elaborates on each of the three ways that teachers can think about problem solving. The article can be printed in rich text format.
In this problem students apply basic proportional reasoning in the context of a pie recipe. Given a recipe for 80 pies, Peter needs to determine whether the ingredients he has on hand are enough to make 2 pies. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension, and printable lists of ingredients (doc).
This brief article describes some of the mathematics of Pythagoras and his society. It relates what they believed to be the natural significance of numbers and the well-known Pythagorean Theorem. A link to a printable page is included.