compare, estimate, and determine measurements in various contexts
use appropriate metric units to estimate and measure length, area, mass, and capacity
Have students work in pairs to select one object in the classroom that is “very small” and one object in the classroom that is “very large”. They could identify the measurable attributes of these objects – do they have length? mass? capacity? area? – and decide what units should be used to measure these attributes. Support students in recognizing that the choice of units is based on several factors, not just the size of the object. After they choose an appropriate unit, have students use benchmarks to estimate the measurements of these attributes and then measure the different attributes of the object as accurately as a purpose requires, recognizing that some attributes may be too challenging to measure (although some students might find creative ways to approximate or research these measures). For example, students might decide to measure different attributes of a reading table or the teacher’s desk.
Provide a variety of measurement scenarios, for example:
Support students in making connections to the science and technology curriculum, where they are investigating mass, volume, solids, liquids, and gasses.
solve problems that involve converting larger metric units into smaller ones, and describe the base ten relationships among metric units
Have students discuss whether given statements, such as those below, are true or false. Have them explain their rationale using their knowledge of metric prefixes and a unit’s size; their understanding of place value; and their mental math strategies for multiplying by 10, 100, or 1000. Have them estimate whether the result will be larger or smaller and describe how many times greater one unit is than the other.
Have students find interesting measurement statistics about animals or people (e.g., how far can a grasshopper jump? how much can a weightlifter lift?). Have students express these measurements in different metric units and discuss the impact of choosing that unit (e.g., if a skunk can spray 4.5 m, what is the effect of saying it can spray 450 cm or 4500 mm?). Also, have them apply proportional reasoning to solve problems such as: After 4 hops, a grasshopper is 1 m from its starting position. How many centimetres is the grasshopper from the starting position after 20 hops? As an extension, students could apply proportional reasoning and express these measurements using related but creative non-standard units (e.g., an Olympic long jumper can jump more than 28 grasshopper hops).
Support students in making connections to the science and technology curriculum; for example, making models of organs or components of body systems.
compare angles and determine their relative size by matching them and by measuring them using appropriate non-standard units
Have students build an “angle-capturing tool” by joining two arms (paper, geo strips, cardboard) with some type of pivot (e.g., a paper fastener, or a nut and bolt). Demonstrate how they can adjust the arms of the tool to match and “capture” the size of an angle. Have them match and compare captured angles to any other angles. They can use their angle-capturing tool to record the size of their captured angles in their notebook; classify them as acute, right, obtuse, or straight; and order them from largest to smallest.
Have students use a tan rhombus pattern block as a non-standard unit to measure the angles of the other pattern blocks. Support them as they notice how many tan wedges fit into an angle, and recognize, for example, that each angle on the green triangle pattern block is equivalent to two tan wedges, and that the angles on the orange square are equivalent to three tan wedges. Next, have them predict the number of tan wedges needed to measure and compare the angles of other shapes. Have them extend this learning by using their non-standard tan wedge to measure the angles “captured” with their angle-capturing tool in Sample Task 1. Guide them to recognize that the use of a unit, like the tan wedges, enables a move from comparing angles (Sample Task 1) to measuring angles (Sample Task 2). Through the use of a unit, the question can change from “Which angle is bigger?” to “How big?” and “How much bigger?”.
Provide students with a cut-out circle. Have them fold the circle in half until they have a very small sector. Have them use this sector as a non-standard measuring tool to compare the sizes of angles for various shapes.
explain how protractors work, use them to measure and construct angles up to 180°, and use benchmark angles to estimate the size of other angles
Ask students how many tan wedges are needed to form a straight line. Guide them to make the connection that every straight line is 180°, so each wedge is 30°. Have them determine the angle measures of the other pattern block pieces in degrees.
To support students to better understand protractors, build on the work they did in E1.4, Sample Task 2 by taping together several tan wedges to make a semi-circular protractor (e.g., six tan wedges = a straight angle). To keep track of the count of wedges, have students create a scale that counts the wedges (e.g., from 0 to 6), and, since angles can open in any direction, have them number the wedges in both directions. This simulates the double scale on a standard protractor.
To make a transparent non-standard protractor (e.g., one where it is easier to recognize the angle beneath the protractor), have students fold a circular piece of wax paper into sectors and number the scale with a marker. Discuss whether the numbers should be placed on the lines or the spaces (they can think about a ruler for a comparison), and have them use their non-standard protractors to describe how much bigger one angle is than another. In consolidating the learning from the task, guide students to compare their non-standard protractors to standard semi-circular protractors and note similarities and differences. Guide students to notice that degrees are simply really small sectors and that, instead of 6 tan wedges fitting into a straight line, it takes 180° to fill that space.
To further understand how a protractor works, have students compare different types of standard protractors (semi-circular variations; angle rulers; circular protractors) and explain similarities and differences. Have them use different protractors to measure the angles of real-life and relevant objects and estimate to verify that the measurements are reasonable.
Have students randomly select an acute angle measure. Have them sketch that angle. Next, have them use the protractor to determine how close their drawing is to the actual angle. Repeat this activity for obtuse angles.
use the area relationships among rectangles, parallelograms, and triangles to develop the formulas for the area of a parallelogram and the area of a triangle, and solve related problems
Have students compare the area of a rectangle to the area of several parallelograms drawn on grid paper, all with the same base length and height (although very different side lengths or “slant lengths”). Support students as they visualize and make predictions about the various areas. Encourage them to check their predictions by counting the squares in each of the shapes and by decomposing the shapes and rearranging the parts. Guide them to recognize that the area of a rectangle is the same as the area of a parallelogram with the same base and height. Reinforce that, regardless of how the parts of the parallelograms were rearranged, their areas are unchanged (conservation of area).