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8.G.A.1 | Warm-up
In this activity, students get their first formal introduction to the idea of mirror orientation, sometimes called “handedness” because left and right hands are reflections of each other. The easiest way to decide which are the right hands is to hold one’s hands up and rotate them until they match a particular ... |
3.MD.D.8 | Narrative
This info gap activity gives students a chance to understand that given the area and one side length of a rectangle, the perimeter can be found, and that given the perimeter and one side length of a rectangle, the area can be found. In both cases, students need to find the missing side length to solve the pro... |
5.NF.B.4 | Narrative
The purpose of this Number Talk is for students to demonstrate strategies and understandings they have for fraction multiplication. The whole number 60 is intentionally selected to represent the minutes in an hour.
These understandings help students develop fluency and will be helpful in this lesson when stud... |
8.F.A.1 | Warm-up
The purpose of this warm-up is for students to notice and describe the features of graphs using their own language. Students will encounter a variety of graphs over the next several lessons and throughout these lessons they will gradually develop more precise language around graphs as the needs of activities di... |
F-IF.C.8a | Activity
This activity introduces students to the
vertex form
. Students examine the parameters in expressions of this form and the graphs of functions defined by such expressions. They look for structure in the given representations and notice that there are connections between the numbers in each expression and the v... |
8.EE.C.7b | Problem 1
The length of a rectangle is 3 cm less than twice the width of the rectangle. If the perimeter is 75 cm, what are the dimensions of the rectangle?
Problem 2
After collecting coins for a month, you count them to see how much money you have. You determine that you have 12 fewer quarters than you have nickels, a... |
5.MD.A.1 | Warm-up
This warm-up prompts students to reason about appropriate units of measurement in estimation and to review related work in grade 5 (converting across different-sized standard units within a given measurement system and using conversions to solve multi-step, real-world problems). It also allows them to form a re... |
F-BF.B.3 | Task
Let $f$ be the function defined by $f(x) = 2x^2 + 4x - 16$. Let $g$ be the function defined by
\begin{align} g(x) &= 2(x+1)^2 - 18 . \end{align}
Verify that $f(x) = g(x)$ for all $x$.
In what ways do the equivalent expressions $2x^2 + 4x - 16$ and $ 2(x+1)^2 - 18$ help to understand the function $f$?
Consider the ... |
A-REI.C.6 | Optional activity
This optional activity gives students another opportunity to apply what they learned about the features of systems of linear equations with one solution, zero solutions, and many solutions. In earlier activities, students were given systems of equations and were asked to determine the number of soluti... |
6.EE.A.2c | Warm-up
The purpose of this algebra talk is to elicit strategies and understandings students have for evaluating an expression for a given value of its variable. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to evaluate expressions.
Launch... |
G-SRT.C.7 | Problem 1
Below are three right triangles. Assume the value of the hypotenuse of each triangle is
$$1$$
.
###IMAGE0###
a) Using what you know about special right triangles, find the length of each side.
b) Fill in the chart describing the sine and cosine of each measure below.
###TABLE0###
Problem 2
Using the cosine an... |
7.RP.A.2 | Activity
This activity provides the first example in this unit of a relationship that is not proportional. The second question focuses students’ attention on the unit rates. If the relationship were proportional then regardless of the number of people in a vehicle, the cost per person would be the same. The question ab... |
6.SP.B.5d | Activity
This activity allows students to practice calculating MAD and build a better understanding of what it tells us. Students continue to compare data sets with the same mean but different MADs and interpret what these differences imply in the context of the situation.
Launch
Arrange students in groups of 3–4. Befo... |
7.G.B.4 | Optional activity
In the previous lesson, students tried using simple methods and tools to measure long distances. In this activity, they learn that a trundle wheel is a tool used in real-world situations to measure such distances. From an image and a description of what a trundle wheel looks like, students think about... |
1.OA.D.8 | Narrative
The purpose of this activity is for students to choose from activities that offer practice adding and subtracting. Students choose from any stage of previously introduced centers.
Five in a Row
How Close?
Number Puzzles
Required Materials
Materials to Gather
Materials from previous centers
Required Preparatio... |
5.NBT.B.5 | Narrative
The goal of this activity is to use the standard algorithm to find products in which composition of a new unit happens once. Students first calculate a 3-digit and 2-digit example using a strategy of their choice and then analyze the same example done with composition recorded above the product. Students may... |
4.NF.B.4a | Narrative
The purpose of this activity is for students to interpret situations involving equal groups of a fractional amount and to connect such situations to multiplication of a whole number by a fraction (MP2).
Students write expressions to represent the number of groups and the size of each group. They reason about ... |
F-IF.C.7a | Activity
This activity is an opportunity to practice using graphing technology to determine important points on a graph and to practice writing a function to represent a situation described verbally. Students can choose to find the coordinates of the intercepts either by using the technological tool or by reasoning abo... |
3.MD.A.2 | Narrative
The purpose of this warm-up is to introduce the context of carnival games and have students consider the elements that make a good game. While students may notice and wonder many things about these images, constraints that make a game challenging, rules that make the game fair, and the way someone can win the... |
4.NF.A | Stage 4: Fractions with Denominators 5, 8, 10, 12, 100
Required Preparation
Materials to Copy
Blackline Masters
Mystery Number Stage 4 Gameboard
Narrative
Students choose a mystery fraction (with a denominator of 5, 8, 10, 12, or 100) from the gameboard. Students give clues based on the given vocabulary.
|
3.OA.C.7 | Stage 1: Factors 1–5 and 10
Required Preparation
Materials to Gather
Paper clips
Two-color counters
Materials to Copy
Blackline Masters
Five in a Row Multiplication and Division Stage 1 Gameboard
Narrative
Students multiply using factors of 1–5 and 10. Partner A chooses two numbers and places a paper clip on each numb... |
7.G.B.5 | Problem 1
Use the diagram below to answer the questions.
###IMAGE0###
a. Name an acute angle.
b. Name an obtuse angle.
c. Name a right angle.
d. Name two adjacent angles.
e. Name two nonadjacent angles.
Problem 2
Two angle diagrams are shown below. Use the information about each diagram to find the measure of... |
1.NBT.C.4 | Narrative
The purpose of this True or False is to elicit strategies students have for using place value understanding to add. These understandings help students deepen their understanding of the properties of operations and will be helpful later when students add within 100.
Launch
Display one statement.
“Give me a sig... |
2.MD.D.9 | Narrative
The purpose of this activity is for students to plot their measurement data and to use the data to answer questions (MP2). In the activity synthesis, students share the methods they use to add or subtract within 20 and discuss different ways that they can use the data in a line plot.
MLR2 Collect and Display.... |
6.RP.A.3 | Activity
The purpose of this activity is for students to practice labeling the tick marks on a double number line diagram with equivalent ratios. This activity revisits a familiar context from a previous lesson so students can apply reasoning about different sized batches of a recipe to help them understand the more ab... |
8.G.A.1a | Optional activity
Up to this point, students have mostly worked with simple figures, that is, figures which are individual and complete and not naturally divided into parts. In this activity, students examine two figures made out of disjoint pieces: the outline of a face, two eyes, and a mouth. The disjoint pieces are ... |
K.NBT.A.1 | Narrative
The purpose of this How Many Do You See is to allow students to use subitizing or grouping strategies to describe the images they see. Students have an opportunity to look for and make use of structure (MP7) because the 10-frame helps students see numbers 11–19 as ten ones and some more ones.
Launch
Groups of... |
4.NBT.B.5 | Zora solves 12 × 64 using an area model.
###IMAGE0###
Use the same reasoning as Zora to solve 35 × 19. Find each partial product in the area model and then fill in the blanks to complete the equation.
###IMAGE1###
|
3.MD.D.8 | Narrative
The purpose of this activity is for students to differentiate methods for finding perimeter from those for finding area. While addition and multiplication are both involved in various ways, students need to understand the problem situation and think about whether the operations performed will provide the desi... |
A-APR.A | Warm-up
The purpose of this warm-up is to elicit the idea that we can use long division to divide polynomials similarly to how we have used long division to divide numbers. While students may notice and wonder many things about these images, relationships between the division steps for the integers and the division ste... |
1.OA.D.8 | Stage 1: Within 10
Required Preparation
Materials to Copy
Blackline Masters
Number Puzzles Addition and Subtraction Stage 1 Gameboard
Number Puzzles Digit Cards
Narrative
Students work together to use digit cards to make addition and subtraction equations within 10 true. Each digit card may only be used one time on a ... |
K.OA.A.3 | Stage 1: Numbers to 9
Required Preparation
Materials to Gather
Connecting cubes
Two-color counters
Materials to Copy
Blackline Masters
Make or Break Apart Numbers Stage 1 Number Mat 4 - 9
Make or Break Apart Numbers Stage 1 Recording Sheet
Make or Break Apart Numbers Stage 1 Dot Page
Narrative
Students roll to get a n... |
A-REI.C.6 | Activity
In this activity, students practice using algebra to solve systems of linear equations in two variables and checking their solutions. Students do not have to use elimination, but the equations in the first three systems conveniently have opposites for the coefficients of one variable, so one variable can be ea... |
F-LE.A.1 | Chain emails are emails with a message suggesting you will have good luck if you forward the email on to others. Suppose a student started a chain email by sending the message to 3 friends and asking those friends to each send the same email to 3 more friends exactly 1 day after receiving it.
Write a function to repres... |
8.EE.C.7a | Activity
Students who pause to think about the structure of a complex equation before taking steps to solve it can find the most efficient solution paths and, sometimes, notice that there is no single solution to be found. The goal of this lesson is to encourage students to make this pause part of their routine and to ... |
A-CED.A.2 | In Class Launch
Use after Unit 7, Lesson 2
Ask students if they have been to a concert or a similar event before. Invite students to share what the experience was like. For example, where was the event? Were a lot of other people there? Who was performing?
Then ask students what they would need to think about if they w... |
8.EE.A.1 | Task
In this problem $c$ represents a positive number.
The quotient rule for exponents says that if $m$ and $n$ are positive integers with $m>n$, then $$\frac{c^m}{c^n} = c^{m-n}.$$ After explaining to yourself why this is true, complete the following exploration of the quotient rule when $m\leq n$:
What expression doe... |
3.NBT.A.2 | Problem 1
Solve. Show or explain your work.
a.
$$479+53=$$
__________
b. __________
$$ =268 + 547$$
c. __________
$$- 195 = 406$$
Problem 2
The third-grade class sells brownies to raise funds. After selling 67 brownies in 1 week, they still have 35 brownies left. How many brownies did they have at the beginning?
|
F-TF.A.1 | Problem 1
Evaluate the following trigonometric expressions and explain how you used the unit circle to determine your answer.
a.
$${\mathrm{sin}\left(\pi+\frac{\pi}{3}\right)}$$
b.
$${\mathrm{cos}\left(2\pi-\frac{\pi}{6}\right)}$$
Problem 2
Corinne says that for any real number
$${\theta}$$
,
$$\mathrm{cos}{\theta}=\ma... |
3.NF.A | Stage 3: Fractions with Denominators 2, 3, 4, 6
Required Preparation
Materials to Copy
Blackline Masters
Mystery Number Stage 3 Gameboard
Narrative
Students choose a mystery fraction (with a denominator of 2, 3, 4, or 6) from the gameboard. Students give clues based on the given vocabulary.
|
6.G.A.1 | Activity
This activity serves several purposes: to allow students to practice creating scale drawings at given scales, to draw attention to the size of the scale drawing as one of the values in the scale changes, and to explore more fully the relationship between scaled area and actual area.
Each group member uses a di... |
6.G.A.1 | Task
Explain why the right triangle shown has an area of exactly 20 square units.
###IMAGE0###
The "legs" of a right triangle are the two sides that form the right angle. If one leg of a right triangle is 5 units long, explain what else would have to be true about the right triangle in order for its area to be 30 squar... |
8.F.B | Optional activity
This activity is optional. The purpose of this activity is for students to examine how changing the input of a non-linear function changes the output. In this activity, students consider how the volume of a rectangular prism with a square base and a known height of 11 units changes if the edge length... |
6.SP.B.5c | Optional activity
The purpose of this activity is to get students to calculate and describe the mean absolute deviation. Students are given a data set and an organizer for calculating the MAD. Then, they consider questions that are intended to get them thinking about MAD more conceptually as a measure of variability.
L... |
5.NBT.A.3 | Narrative
The purpose of this activity is for students to use place value understanding to find decimals that are greater than or less than given numbers. Students work with the frisbee context from the previous activity. They choose decimals for possible distances which are in between the given distances of frisbee th... |
1.NBT.B.2a | Narrative
The purpose of this activity is for students to represent a two-digit number in multiple ways. Students do not need to come up with every way, but they may find a method that results in them doing so. Students may choose to use connecting cubes as they work and then show their thinking with drawings, numbers,... |
S-CP.A.1 | You flip a coin three times in a row. Your friend tells you that the sample space for your experiment is just “head/tails.” You know he is incorrect.
Represent the sample space of this experiment visually to help convince your friend, and explain your reasoning.
Is there another way to represent this sample space? Why ... |
S-IC.B.3 | Task
The following are some common methods of data collection in statistical studies that involve people.
Broadly speaking, a survey is a way of learning about a group of people by having some of the people in the group answer questions. A survey might involve completing a form, completing a questionnaire online, parti... |
7.RP.A.2 | Activity
Prior to this lesson, students have seen that right triangles with a horizontal side, a vertical side, and a long side along the same line are all similar. This activity exploits this structure to examine the coordinates of points lying on a particular line. The discussion then produces an equation for the lin... |
K.OA.A.5 | Narrative
The purpose of this How Many Do You See is for students to subitize or use grouping strategies to describe the images they see.
Launch
Groups of 2
“How many do you see? How do you see them?”
Flash the image.
30 seconds: quiet think time
Activity
Display the image.
“Discuss your thinking with your partner.”
1 ... |
8.EE.B.5 | Activity
Building off the work in the previous activity, students now graph a proportional relationship on two differently scaled axes and compare the proportional relationship to an already-graphed non-proportional relationship on the same axes. Students are asked to make sense of the intersections of the two graphs b... |
5.MD.C.5b | Narrative
The purpose of this activity is for students to recognize that a base of a prism is a two-dimensional rectangle and any face of a prism can be a base. Students may start with a possible rectangular base and try to visualize which face of a given prism matches the base or they may start with the prism, study t... |
F-BF.B.4 | Activity
In this activity, students revisit the same function they saw in the warm-up, which was given in function notation. They work to find and represent the inverse function and think about what it tells us in this situation.
Launch
Point out to students that the equations we have seen in the past few lessons use v... |
4.NBT.B.6 | Problem 1
Solve. Show or explain your work. Then check your work.
a.
$${48\div4}$$
b.
$$67\div2$$
Problem 2
Enter the unknown number that makes the equation true.
$$38 = 12 \times 3 \ +$$
_____
Problem 3
Choose the division expression below that corresponds with the multiplication equation in Problem 2.
|
8.NS.A.1 | Activity
The purpose of this activity is for students to learn and practice a strategy for rewriting rational numbers with decimal representations that repeat eventually into their fraction representations. Students begin by arranging cards in order that show how the strategy was used to show
\(0.4\overline{85}=\frac{4... |
4.NF.B | Warm-up
The purpose of this Math Talk is to elicit strategies and understandings students have for decomposing fractions into a unit fraction times a whole number and using the associative and commutative properties. These understandings help students develop fluency and will be helpful later in this lesson when studen... |
G-CO.A.1 | Activity
In this activity, students write out a description of a parallelogram’s rotation symmetry. This invites students to apply the definition of rotation.
Launch
Representation: Access for Perception.
Read the situation aloud. Students who both listen to and read the information will benefit from extra processing t... |
6.NS.B.4 | Optional activity
This game provides an opportunity for students to review factors and multiples. There are two versions of the game:
Version A, “10 Anywhere”: The teacher mixes the calling cards and randomly selects one at a time. Upon selecting the card, the teacher reads the statement out loud and records it on the ... |
S-IC.A.2 | Activity
The mathematical purpose of this activity is to make, critique, and justify claims using the data-generating process. The situation involves questioning whether the apparent disproportionate representation of a sample is due to bias or random selection. Students perform a simulation to determine how often the ... |
K.CC.B.4 | Narrative
The purpose of this warm-up is to allow students to connect language to mathematical representation, and consider different representations for the same quantity. This will be useful when students need to create and compare representations of quantities in a later activity. This warm-up gives students opportu... |
K.CC.B.5 | Narrative
The purpose of this warm-up is for students to consider concepts of number in a familiar context. Students may use the structure of the chart to determine how many students made each choice (MP7). In this warm-up, students count two groups to find the total. Students have an opportunity to hear and practice t... |
8.NS.A.1 | Problem 1
Which of the rational numbers have a terminating decimal expansion? Select all that apply.
Problem 2
What is the decimal expansion of
$$\frac{167}{6}$$
?
|
8.G.A.5 | Activity
This activity could be done on a sunny day. You should try it out ahead of time to ensure that the shadows created in your part of the world at the time your class takes place are cooperative! Either find a tall object outside that all students will find the height of, or let students choose a tall object (for... |
K.CC | Narrative
The purpose of this How Many Do You See is for students to subitize or use grouping strategies to describe the images they see. Recognizing and describing one more than a given quantity will be useful in the next section when students work on creating and identifying one more than a given quantity or number.
... |
A-CED.A.1 | Activity
In this activity, students return to the framing problem they encountered when starting the unit. In that first lesson, they were challenged to use an entire sheet of paper to frame a picture and ensure that the thickness is uniform all around. At that time, students did not have adequate knowledge to solve th... |
1.NBT.A.1 | Narrative
The purpose of this Choral Count is to invite students to practice counting backward by 1 and notice patterns in the count. These understandings help students develop fluency with the count sequence as well as the base-ten structure of numbers.
Launch
“Count backward by 1, starting at 100.”
Record as students... |
4.NBT.B.5 | Narrative
When using an algorithm that uses partial products, students may be inclined to pay attention only to single digits in each number and pay little attention to the value of the digits. For example,
\(32 \times 19\)
might sound like “9 times 2 is 18 and 9 times 3 is 27.” In this activity, students analyze this ... |
5.NF.B.4a | Task
The diagram below represents one whole.
###IMAGE0###
Part One
Write a multiplication story that could be solved using the diagram with its two types of shading. Explain how your story context relates to the diagram provided.
Part Two
Write the equation that represents this situation. Explain how your equation rel... |
4.MD.A.1 | Optional activity
This task is an opportunity to assess students’ prior knowledge of standard units of length and find out the kinds of objects students already use as benchmarks for estimating length units.
Note that groups will likely produce their length of string pretty quickly. The majority of the time in this act... |
6.EE.A.1 | Activity
The purpose of this task is to give students experience working with exponential expressions and to promote making use of structure (MP7) to compare exponential expressions. To this end, encourage students to rewrite expressions in a different form rather than evaluate them to a single number.
For students who... |
6.NS.B | Optional activity
In this Fermi problem, students estimate the total volume occupied by all of the breakfast cereal purchased in a year in the United States.
Monitor for different approaches to solving the problem, and select students to share during the discussion. In particular, look for:
A range of estimates
Differe... |
K.CC.A.3 | Task
Materials
Each pair of students needs: * One worksheet * Two markers of different colors * One pair of dice
Action
Student A rolls the two dice, finds the sum, and traces the number on the worksheet which corresponds to the answer with his/her marker. Student A then passes the dice to Student B who rolls both the ... |
8.NS.A.1 | Task
Represent each of the following rational numbers in fraction form.
$0.33\overline{3}$
$0.3\overline{17}$
$2.1\overline{6}$
|
2.NBT.B.5 | Problem 3
Pre-unit
Find the value of each sum or difference. Show your thinking.
\(52 - 43\)
\(65 - 19\)
\(36 + 47\)
|
1.NBT.C.5 | Narrative
The purpose of this activity is for students to choose from activities that offer practice working with tens and ones. Students choose from any stage of previously introduced centers.
Grab and Count
Five in a Row
Check It Off
Required Materials
Materials to Gather
Materials from previous centers
Required Prep... |
4.MD.C.7 | Narrative
Previously, students found numerous angle sizes by reasoning and without using a protractor. They have done so with problems with and without context. In this activity, students consolidate various skills and understandings gained in the unit and apply them to solve problems that are more abstract and complex... |
7.EE.B.3 | Activity
This activity offers four word problems. Depending on time constraints, you may have all students complete all four problems or assign a different problem to each group. The problems increase in difficulty. It is suggested that students create a visual display of one of the problems and do a gallery walk or pr... |
N-CN.A.2 | Task
For each odd positive integer $n$, the only real number solution to $x^n = 1$ is $x = 1$ while for even positive integers $n$, $x = 1$ and $x = -1$ are solutions to $x^n = 1$. In this problem we look for all complex number solutions to $x^n = 1$ for some small values of $n$.
Find all complex numbers $a + bi$ whose... |
3.NBT.A.2 | Stage 6: Add Hundreds, Tens, or Ones
Required Preparation
Materials to Gather
Number cubes
Materials to Copy
Blackline Masters
Target Numbers Stage 6 Recording Sheet
Narrative
Students add hundreds, tens, and ones to get as close to 1,000 as possible. Students start by rolling three number cubes to get a starting numb... |
5.MD.C.3b | Optional activity
This activity clarifies the distinction between volume and surface area and illustrates that two polyhedra can have the same volume but different surface areas.
Students build shapes using two sets of eight cubes and determine their volumes and surface areas. Since all of the designs are made of the s... |
5.G.B.4 | Task
Niko and Carlos are studying parallelograms and trapezoids. They agree that a parallelogram is a quadrilateral with two pairs of parallel sides. Niko says,
A trapezoid has one pair of parallel sides and a parallelogram has two pairs of parallel sides. So a parallelogram is also a trapezoid.
Carlos says,
No - a tra... |
3.MD.B.3 | Narrative
The purpose of this activity is for students to use data presented in scaled bar graphs to solve one-step “how many more” and “how many fewer” problems. Students use scaled bar graphs that they created in the previous lesson that contain data about the favorite time of the year. Answering questions about a gr... |
A-REI.B.4b | Optional activity
In this optional activity, students investigate how the parameters in a quadratic equation affect the number of solutions and the kinds of solutions. Students are first given the equation
\(4x^2 + bx + 9=0\)
and are asked to find a value of
\(b\)
that would produce a certain number or kind of solution... |
G-CO.B.8 | Activity
In a previous lesson, students matched diagrams to conjectures. In this lesson, they identify the given information and the statement to prove in the conjectures. For example, “all rhombuses are parallelograms” might turn into “show that in quadrilateral
\(ABCD\)
, with segments
\(AB\)
,
\(BC\)
,
\(CD\)
, and
... |
G-SRT.B.4 | Task
Below is a picture of a right triangle $ABC$ with right angle $C$ along with the point $D$ so that $\overleftrightarrow{CD}$ is perpendicular to $\overleftrightarrow{AB}$.
###IMAGE0###
Show that $\triangle ACB$ is similar to $\triangle ADC$ and to $\triangle CDB$.
Use part (a) to conclude that $|AC|^2 + |BC|^2 = |... |
6.G.A.1 | Optional activity
In this activity, students determine the area of an unfamiliar polygon and think about various ways for doing so. The task prepares students to find the areas of other unfamiliar shapes in real-world contexts. It also reinforces the practice of sense-making, planning, and persevering when solving a pr... |
4.MD.C.7 | Task
Draw an angle that measures 60 degrees like the one shown here:
###IMAGE0###
Draw another angle that measures 25 degrees. It should have the same vertex and share side $\overrightarrow{BA}$.
How many angles are there in the figure you drew? What are their measures?
Make a copy of your 60 degree angle. Draw a diffe... |
F-IF.C.7 | Activity
The goal of this activity is for students to graph polynomial equations to develop their understanding of the different features the graph representing a polynomial can have and to begin to connect the structure of the expression to the shape of the graph. This activity is meant to be an informal study in whic... |
F-IF.B.4 | Activity
In this activity, students examine graphs of functions, identify and describe their key features, and connect these features to the situations represented. These key features include the horizontal and vertical intercepts, maximums and minimums, and intervals where a function is increasing or decreasing (or wh... |
4.MD.C.5 | Narrative
Students commonly think that angles formed by longer segments are greater in size than those formed by shorter segments. The purpose of this warm-up is to bring up and address this likely misconception. The diagrams prompt students to observe the lengths of segments forming the angles and consider how they af... |
A-APR.D.6 | Problem 1
What should you do to turn this function into a proper rational function?
$${f(x)={x^3-4x\over{x^2}}}$$
Problem 2
How are the horizontal and vertical asymptotes different or similar in each of the following functions? Compare both algebraically and graphically.
$${f(x)={x^3-4\over{x^4}}}$$
$${g(x)={x^3-4\over... |
F-BF.B.4c | Task
The table below shows $R=f(t)$, the total amount of rain, in centimeters (cm), during a steady rainfall as a function of time, $t$, in minutes, since the rain started.
###TABLE0###
Explain why $f$ is an invertible function.
Find $f(45)$ and interpret it in the context of the situation.
Find $f^{-1}(4.2)$ and inter... |
5.NF.B.5 | Task
Your classmate Ellen says,
When you multiply by a number, you will always get a bigger answer. Look, I can show you.
Start with $9$.
Multiply by $5$. $\hskip 70pt 9 \times 5 = 45$
The answer is $45$, and $\hskip 35pt 45 > 9$
$45$ is bigger than $9$.
It even works for fractions.
Start with $\frac12$.
Multiply by ... |
F-IF.B.4 | Activity
In this activity, students match four descriptions of situations characterized by exponential change with four graphs. In order to make a correct match, students will need to attend to whether the growth factor is greater than 1 or less than 1, and determine the growth factor from the graph with enough precisi... |
8.EE.A.3 | Activity
In this info gap activity, students continue to use scientific notation as a tool for working with small and large numbers—to describe quantities, make estimates, and make comparisons (e.g., to express how many times as much one is as the other).
The info gap structure requires students to make sense of proble... |
7.NS.A | Warm-up
This warm-up encourages students to reason algebraically about various computational relationships and patterns. While students may evaluate each side of the equation to determine if it is true or false, encourage students to think about the properties of arithmetic operations in their reasoning.
Seeing the str... |
5.NBT.A.4 | Narrative
The purpose of this activity is for students to practice rounding numbers to the nearest whole, tenth, or hundredth. Students may choose to use a number line or any other strategy that makes sense to them.
Launch
Groups of 2
Activity
5 minutes: independent work
2 minutes: partner discussion
Monitor for studen... |
F-IF.B.5 | Activity
In this activity, students describe situations based on the graph then identify examples of values that are in the domain and range or not. In the associated Algebra 1 lesson, students describe the domain and range of functions from graphs. Students are supported with this activity by focusing on single values... |
1.OA.C.6 | Narrative
The purpose of this activity is for students to learn stage 3 of the Five in a Row center. Students choose to add 7, 8, or 9 to the number on their card and then place their counter on the sum on the gameboard.
The first partner to have five counters in a row wins.
MLR8 Discussion Supports.
Synthesis: For eac... |
F-LE.A.4 | Warm-up
In this warm-up, students practice evaluating and comparing logarithms. Except for one that requires estimation, all logarithms can be found mentally.
Students may need to rewrite some of the logarithms involving decimal numbers in order to better see the value of the logarithm. For example, they may find it he... |
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