This short video and interactive assessment activity is designed to teach fourth graders about comparing decimals with whole numbers using inequalities.
This task gives students an opportunity to work with exponential functions in a real world context involving continuously compounded interest. They will study how the base of the exponential function impacts its growth rate and use logarithms to solve exponential equations.
The purpose of this task is for students to compare fractions using common numerators and common denominators and to recognize equivalent fractions.
This short video and interactive assessment activity is designed to teach fifth graders about comparing fractions using lcm - word problems.
This short video and interactive assessment activity is designed to teach fifth graders about comparing fractions using a fraction bar illustration.
This task is meant to address a common error that students make, namely, that they represent fractions with different wholes when they need to compare them. This task is meant to generate classroom discussion related to comparing fractions. Particularly important is that students understand that when you compare fractions, you implicitly always have the same whole.
This video explains how to compare fractions with the different denominators using modeling.
This video explains how to compare fractions with the same denominators using the meaning of a fraction.
This video explains how to compare fractions with the same numerators without using the LCD.
This task is appropriate for assessing student's understanding of differences of signed numbers. Because the task asks how many degrees the temperature drops, it is correct to say that "the temperature drops 61.5 degrees." However, some might think that the answer should be that the temperature is "changing -61.5" degrees. Having students write the answer in sentence form will allow teachers to interpret their response in a way that a purely numerical response would not.
The purpose of this task is to foster a classroom discussion that will highlight the difference between multiplicative and additive reasoning.
The purpose of this task is to assess studentsŐ understanding of multiplicative and additive reasoning.
Unit 8: Data Sets and Distribution
Lesson 14: Comparing Mean and Median
In this lesson, students investigate whether the mean or the median is a more appropriate measure of the center of a distribution in a given context. They learn that when the distribution is symmetrical, the mean and median have similar values. When a distribution is not symmetrical, however, the mean is often greatly influenced by values that are far from the majority of the data points (even if there is only one unusual value). In this case, the median may be a better choice.
At this point, students may not yet fully understand that the choice of measures of center is not entirely black and white, or that the choice should always be interpreted in the context of the problem (MP2) and should hinge on what insights we seek or questions we would like to answer. This is acceptable at this stage. In upcoming lessons, they will have more opportunities to include these considerations into their decisions about measures of center.
These word problems involve multiplicative comparison.
Students will compare data for two states using comparison symbols and both rounded and unrounded (exact) numbers. Students will then write their own question to compare the data.
Unit 7: Rational Numbers
Lesson 7: Comparing Numbers and Distance from Zero
In this lesson, students use precise language to distinguish between order and absolute value of rational numbers (MP6). It is a common mistake for students to mix up “greater” or “less” with absolute value. A confused student might say that -18 is greater than 4 because they see 18 as being the “bigger” number. What this student means to express is I-18I > 4. The absolute value of -18 is greater than 4 because -18 is more than 4 units away from 0. In the “Submarine” activity, students visualize possible elevations of characters with sticky notes on a vertical number line. The freedom to move a sticky note within a specified range anticipates the concept of a solution to an inequality in the next section.
This short video and interactive assessment activity is designed to teach second graders about comparing pints and quarts by pictures.
Unit 7: Rational Numbers
Lesson 3: Comparing Positive and Negative Numbers
Returning to the temperature context, students compare rational numbers representing temperatures and learn to write inequality statements that include negative numbers. Students then consider rational numbers in all forms (fractions, decimals) and learn to compare them by plotting on a number line and considering their relative positions. Students abstract from “hotter” and “colder” to “greater” and “less,” so if a number a is to the right of a number b, we can write the inequality statements a>b and $b\text-100$. Students are briefly introduced to the word sign (i.e., algebraic sign) since it is often used to talk about whether numbers are positive or negative. Students use the structure of the number line to reason about relationships between numbers (MP7).
The purpose of this task is to generate a classroom discussion that helps students synthesize what they have learned about multiplication in previous grades.
This short video and interactive assessment activity is designed to teach third graders about comparing quarts and pints by formula.