The students discover the basics of heat transfer in this activity by constructing a constant pressure calorimeter to determine the heat of solution of potassium chloride in water. They first predict the amount of heat consumed by the reaction using analytical techniques. Then they calculate the specific heat of water using tabulated data, and use this information to predict the temperature change. Next, the students will design and build a calorimeter and then determine its specific heat. After determining the predicted heat lost to the device, students will test the heat of solution. The heat given off by the reaction can be calculated from the change in temperature of the water using an equation of heat transfer. They will compare this with the value they predicted with their calculations, and then finish by discussing the error and its sources, and identifying how to improve their design to minimize these errors.

Welcome to the UnboundEd Mathematics Guide series! These guides are designed to explain what new, high standards for mathematics say about what students should learn in each grade, and what they mean for curriculum and instruction. This guide, the first for Kindergarten, includes three parts. The first part gives a “tour” of the standards for Counting & Cardinality using freely available online resources that you can use or adapt for your class. The second part shows how Counting & Cardinality relate to classification of objects in Kindergarten (K.MD.B). And the third part explains where Counting & Cardinality is situated in the progression of learning in Grades K-2. Throughout all of our guides, we include a large number of sample math problems. We strongly suggest tackling these problems yourself to help best understand the methods and strategies we’re covering, and the potential challenges your students might face.

This is a collection of sample counting circles you can use in your classroom as part of number talks.

Students practice counting sequences by standing in a circle and counting one by one.

Counting Collections is an important mathematical routine that students or families can do with very little guidance at home. Teachers could make kits with available resources for use at home, or send suggestions for commonly found objects that families could use for counting practice at home.

Counting Collections are just as described; they are collections of items that students count. Depending on your students, you will need several different kits. Kits hold several different collections of items.

This short video and interactive assessment activity is designed to teach second graders about counting cubes and creating a place value diagram.

Students who work on this task will benefit in seeing that given a quantity, there is often more than one way to represent it, which is a precursor to understanding the concept of equivalent expressions.

These games support student development of number sense and the concept of mathematical operations

This task gives students another way to practice counting and gain fluency with connecting a written number with the act of counting. This task should be introduced by the teacher and would then be a good independent center.

The most engaging way to practice counting with students is to have them count meaningful things in their lives. Since five-year-olds are very focused on themselves this is easily done by allowing them to count themselves, their friends and objects within the classroom that relate to their daily lives.

This short video and interactive assessment activity is designed to teach first graders about counting rectangles, squares, and triangles in composite figures.

This challenging problem and brainteaser gives first graders an opportunity to compose and decompose squares.

This is an instructional task related to deepening place-value concepts. The important piece of knowledge upon which students need to draw is that 10 tens is 1 hundred.

This short video and interactive assessment activity is designed to teach third graders about counting vertices and sides in various shapes.

The objective of this lesson is to gain automaticity counting to 100 and to establish the importance of multiples of ten. The final goal of this lesson is for students to be able to count by tens and articulate the term for this.

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Ten printable colouring pages which depict the numbers one through ten. Each page has a spelled-out number in Michif, the language of Métis Peoples’, as well as the numerical equivalence. There are also images of culturally significant items on each page, which correspond with the respective number. There are written instructions on the bottom of each page that indicate different activities that supplement the colouring pages.

This task involves solving equations with rational coefficients, and requires students to use the distributive law ("combine like terms"). The equation also provides opportunities for students to observe structure in the equation to find a quicker solution, as in the second solution presented.