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6.NS.C.6b | Activity
The purpose of this task is for students to connect opposite signs in coordinates with reflections across one or both axes. Students investigate relationships between several pairs of points in order to make this connection more generally (MP8). The square grid, spaced in units, means that students can use cou... |
4.NF.B.3c | Narrative
This warm-up prompts students to carefully analyze subtraction expressions containing two fractions or a whole number and a fraction. To compare the values of the expressions, students need to perform subtraction and apply their knowledge of equivalence. The reasoning here will also be helpful later as studen... |
8.EE.C.7b | Problem 1
The average household uses 1400kWh of electricity per month. In one household, air conditioning uses 300kWh per month. Twice as much electricity is used to heat water as to run a refrigerator. 50% of total electricity used goes to miscellaneous uses (like lighting, dishwashers, and TVs).
Assuming this househo... |
3.MD.C.7b | Problem 7
Pre-unit
###IMAGE0###
What is the area of the rectangle? Explain or show your reasoning.
|
G-C.B | Warm-up
This warm-up invites students to reason about areas of circles and their sectors in the context of cost-efficiency. This context will be explored further in the next activity.
Student Facing
At a pizza restaurant, a personal pizza has a radius of 10 centimeters and costs
$
5. Another restaurant takes a pizza wi... |
2.MD.D.9 | Narrative
The purpose of this activity is for students to generate measurement data and represent the data in a line plot. Students measure pencils in centimeters, check the accuracy of their measurements, and use a template to represent their data in a line plot. In the synthesis, students revisit the importance of la... |
7.RP.A.3 | Task
Inflation is a term used to describe how prices rise over time. The rise in prices is in relation to the amount of money you have. The table below shows the rise in the price of bread over time:
###TABLE0###
For the price in each decade, determine what the increase is as a percent of the price in the previous dec... |
2.MD.B.6 | Narrative
The purpose of this activity is for students to learn that numbers are represented on a number line as lengths from 0. Students choose their own length unit to make equally spaced tick marks and label them 0–20. In the synthesis, students compare their number lines and notice that on a given number line the l... |
3.OA.B.5 | Stage 6: Multiply to 3,000
Required Preparation
Materials to Gather
Number cards 0–10
Materials to Copy
Blackline Masters
How Close? Stage 6 Recording Sheet
Narrative
Before playing, students remove the cards that show 10 and set them aside.
Each student picks 6 cards and chooses 4 of them to create a multiplication e... |
A-APR.C.4 | Warm-up
The goal of this activity is for students to follow directions to build several right triangles in order to become familiar with the process and form initial opinions, such as whether or not the instructions will always work (MP1). The following activity builds on the work done here, asking students to write an... |
A-REI.D.12 | Warm-up
In the first activity of the lesson, students consider whether the expression
\(2x+3y\)
is greater than, less than, or equal to 12 for given
\((x,y)\)
pairs. This warm-up familiarizes students with the computation and reasoning that they will need later to determine the solution region of a linear inequality in... |
8.G.A | Activity
In previous lessons, students perform dilations on a circular grid and with no grid. In this activity, they perform dilations on a square grid. A square grid is particularly helpful if the center of dilation and the points being dilated are grid points. When the extra structure of coordinates is added, as in t... |
K.MD.A.2 | Problem 1
Pre-unit
Circle the rectangle that is longer.
###IMAGE0###
Circle the rectangle that is shorter.
###IMAGE1###
|
7.EE.B.3 | Activity
This activity is parallel to one in the previous lesson, except that students are creating a tape diagram after interpreting an equation rather than interpreting a story. The intention is for students to reason in any way that makes sense to them about the equations and diagrams to figure out the solution to e... |
4.NBT.B.6 | Narrative
This warm-up prompts students to analyze patterns and look for structure in division equations (MP7), and to reinforce their understanding of factors and multiples.
Launch
Groups of 2
Display the equations.
“What do you notice? What do you wonder?”
1 minute: quiet think time
Activity
“Discuss your thinking wi... |
4.NBT.B.6 | Narrative
In this activity, students continue to use base-ten representations and to reason about equal-size groups to find whole-number quotients. The work reinforces the idea of decomposing a hundred into 10 tens as needed to perform division.
Students explicitly use place value understanding to decompose hundreds an... |
5.NF.B.4 | Narrative
This Number Talk encourages students to think about the relationship between division and fractions and the order of operations in order to strategically multiply whole numbers by fractions. The strategies elicited here will be helpful later in the lesson when students find the missing value in multiplication... |
6.SP.B.4 | Task
In Mrs. Sanchez' math classroom, more people sit on the right-hand side of the room than the left. The students on the right-hand side of the classroom received the following scores on an exam worth 100 points:
$$ 85,\, 90,\, 100,\, 95,\, 0,\, 0,\, 90,\, 70,\, 100,\, 95,\, 80,\, 95 $$
The students on the left rec... |
6.SP.A.2 | The dot plot below shows the numbers of miles that sixth grade students live from their school.
###IMAGE0###
What is the average number of miles that this group of sixth graders live from school?
|
F-IF.C | Warm-up
In this warm-up, students use the structure of expressions to match equations and graphs of polynomials (MP7). While three of the graphs show end behavior students have encountered in previous lessons, one of the graphs has end behavior the opposite of what they have seen, and this graph matches an equation wit... |
2.MD.D.10 | Narrative
The purpose of this activity is for students to learn a new way of organizing data: a picture graph. In the launch, students engage in a discussion about what they notice about the graph and how a picture graph makes it easier to interpret data. After students discuss the picture graph and consider what they ... |
2.NBT.A.1 | Task
What number represents the same amount as 2 tens + 7 ones?
What number represents the same amount as 4 tens + 0 ones?
What number represents the same amount as 5 tens + 12 ones?
What number represents the same amount as 3 hundreds + 18 tens + 5 ones?
What number represents the same amount as 7 hundreds + 19 tens?
|
7.EE.A.1 | Activity
In the first part of the activity, students apply what they noticed in the previous activity. In the second part, they practice identifying equivalent expressions. This is in preparation for the associated Algebra 1 lesson, when they will need to rewrite expressions in equivalent forms, including expanding exp... |
4.NBT.B.4 | Stage 6: Beyond 1,000
Required Preparation
Materials to Copy
Blackline Masters
Number Puzzles Addition and Subtraction Stage 6 Recording Sheet
Narrative
Students use the digits 0–9 to make addition equations true. They work with sums and differences beyond 1,000.
|
2.NBT.A.1 | Task
The post office packages stamps like this:
10 stamps in each strip.
10 strips of 10 in each sheet.
Yesterday Mike saw 4 full sheets, 7 strips, and 2 extra stamps in the drawer. He counted all the stamps and found out that there were 472 stamps in all. He said,
The number 472 matches the 4 sheets, 7 strips, and 2 s... |
8.EE.A.4 | Task
This headline appeared in a newspaper.
###TABLE0###
Decide whether this headline is true using the following information.
There are about $8\times 10^3$ Giantburger restaurants in America.
Each restaurant serves on average $2.5\times10^3$ people every day.
There are about $3\times10^8$ Americans.
Explain your reas... |
3.OA.D.8 | Narrative
The purpose of this activity is for students to match tape diagrams, equations, and descriptions of situations and explain the connection to model with mathematics (MP4). The situations share the same context and numbers. Students consider how different unknown quantities are reflected in the diagrams, depend... |
4.NBT.A | Stage 5: Six-digit Numbers
Required Preparation
Materials to Copy
Blackline Masters
Mystery Number Stage 5 Gameboard
Narrative
Students choose a mystery number (up to six digits) from the gameboard. Students give clues using the given vocabulary.
|
7.G.B.6 | Activity
In this activity, students practice mentally dissecting a prism with a non-rectangular base into simpler prisms. The dissection corresponds to a dissection of the base into simpler figures. This expands on students’ ability to calculate the area of a base of a figure that has a rectangular base because here th... |
1.MD.A.2 | Narrative
The purpose of this warm-up is to elicit the idea of measuring length with connecting cubes, which prepares students to measure their own shoes and solve story problems about their measurements in the next activity.
Launch
Groups of 2
Display the image.
“What do you notice? What do you wonder?”
1 minute: quie... |
1.NBT.B | Stage 1: Two-digit Numbers
Required Preparation
Materials to Gather
Number cards 0–10
Materials to Copy
Blackline Masters
Mystery Number Stage 1 Directions
Narrative
Students pick two cards and make a mystery two-digit number. Students give clues based on the sentence starters.
|
2.MD.D.10 | Narrative
The purpose for this warm-up is to invite students to notice and wonder about pictures of transportation that will be used later in the lesson. They may notice that all the pictures are forms of transportation that people in the community use to get around. This leads into the next activity, in which students... |
7.RP.A.2 | Activity
In previous lessons, students have seen that corresponding side lengths of similar polygons are proportional. That is, the side lengths in one polygon can be calculated by multiplying corresponding side lengths in a similar polygon by the same scale factor. This activity explores ratios of side lengths
within
... |
7.EE.B.4a | Activity
The purpose of this activity is to practice solving equations of the form
\(p(x+q)=r\)
, recognizing that there are two valid approaches, and making judgments about which one is more sensible for a given equation.
Launch
Display this equation and a hanger diagram to match:
\(3(x+2)=21\)
. Tell students, “Any t... |
1.MD.C.4 | Narrative
The purpose of this activity is for students to represent data in an organized way. In grade 1, students were introduced to each of the representations shown in the Student Responses section below.
Students should have access to tools that may help them represent the data (for example, extra copies of the pic... |
2.OA.B.2 | Stage 4: Subtract within 20
Required Preparation
Materials to Gather
Colored pencils or crayons
Number cards 0–10
Paper clips
Materials to Copy
Blackline Masters
Capture Squares Stage 4 Gameboard
Capture Squares Stage 4 Spinner
Narrative
Students spin to get a number (16–20) and flip a card (0–10). They subtract the n... |
6.SP.A.1 | Task
Which of the following are statistical questions? (A statistical question is one that can be answered by collecting data and where there will be variability in that data.)
How many days are in March?
How old is your dog?
On average, how old are the dogs that live on this street?
What proportion of the students at ... |
8.G.B.6 | Problem 1
Lee tried to use the Pythagorean Theorem on the triangle shown below and found that the relationship did not hold true.
###IMAGE0###
Explain why the Pythagorean Theorem did not show a true relationship in Lee’s triangle.
Problem 2
Which three measures could be the side lengths of a right triangle? Explain or ... |
7.SP.A | Optional activity
This activity is additional practice for students to understand the relationship between a sample and population. It may take additional time, and so is included as an optional activity.
In this activity, students attempt to recreate the data from the population data using three given samples (MP2). I... |
A-SSE.A.2 | Activity
In this activity, students revisit the area model for multiplying binomials by using values in a concrete situation. By focusing on the situation, students can see the relationship between the areas of the subregions and the area of the whole as well as the connection to distributing binomials. In the associat... |
2.NBT.B.7 | Narrative
The purpose of this Number Talk is to elicit strategies and understandings students have for counting back as a strategy for finding the value of differences. These understandings help students develop fluency and will be helpful later in this lesson when students subtract within 1,000. As students share thei... |
6.G.A.1 | Activity
In earlier lessons, students saw that a square can be decomposed into two identical isosceles right triangles. They concluded that the area of each of those triangles is half of the area of the square. They used this observation to determine the area of composite regions.
This activity helps students see that ... |
7.EE.B.4a | Warm-up
Students encounter and reason about a concrete situation, hangers with equal and unequal weights on each side. They then see diagrams of balanced and unbalanced hangers and think about what must be true and false about the situations. In subsequent activities, students will use the hanger diagrams to develop ge... |
8.G.A.1c | Activity
In this activity, students will investigate the question, “What happens to parallel lines under rigid transformations?” by performing three different transformations on a set of parallel lines. After applying each transformation, they will jot down what they notice by answering the questions for each listed tr... |
3.MD.D.8 | Narrative
The purpose of this activity is for students to solve problems that involve perimeter and area (MP2). The problems that students solve involve features that could be present in a park.
Action and Expression: Develop Expression and Communication.
Synthesis: Identify connections between strategies that result i... |
N-Q.A.1 | Activity
In this activity, students provide reasons for a proof that parallel lines must have equal slopes. To prepare them for this reasoning, students begin by noticing and wondering about an image of parallel lines on a coordinate plane. Identify students who annotate their image.
Launch
Display the graph for all to... |
8.EE.C.8b | Problem 1
Small boxes contain Blu-ray disks and large boxes contain one gaming machine. Three boxes of gaming machines and a box of Blu-rays weigh 48 pounds. Three boxes of gaming machines and five boxes of Blu-rays weigh 72 pounds. How much does each box weigh?
Problem 2
A language arts test is worth 100 points. There... |
4.NF.B.3b | Write each mixed number as an equivalent fraction greater than 1. Show or explain your work.
a.
$${3{1\over4}}$$
b.
$${2{3\over5}}$$
c.
$${4{2\over9}}$$
|
5.NF.A.1 | Narrative
The purpose of this activity is for students to make a line plot and answer questions about the data collected. The numbers that students plot come from spinning a spinner twice and adding the fractions on the spinner. The denominators are chosen so that 8 can be used as a common denominator. Students observe... |
G-CO.B.8 | Activity
This activity invites students to convince themselves, then a friend, and then a skeptic that the diagonals of a parallelogram bisect each other. Students can use transformations or congruent triangles to convince a skeptic that the diagonals of a parallelogram bisect each other.
Stating the goal of the proof ... |
3.MD.C.6 | Narrative
The purpose of this activity is for students to see that there are different types of square units that can be used to measure area and that an area with the same number of square units can be larger or smaller depending on the unit that is used. To facilitate comparison, one partner works on inch grid paper ... |
F-BF.B.3 | Warm-up
This warm-up prompts students to carefully analyze and compare properties of graphs, particularly the locations of the intercepts. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminology students know and how they talk about ch... |
3.MD.C.6 | Problem 1
What is the area, in square units, of the rectangle below?
###IMAGE0###
Problem 2
What is the area, in square units, of the rectangle below?
###IMAGE1###
|
A-REI.B.4b | Activity
In this activity, students find solutions to equations from a list of values, then rearrange the equations into functions whose graphs have
\(x\)
-intercepts at the same place as the solutions to the equations. In the associated Algebra 1 lesson, students solve quadratic equations using the factored form. This... |
3.MD.B.4 | Stage 2: Quarter Inches
Required Preparation
Materials to Gather
Objects of various lengths
Rulers (inches)
Materials to Copy
Blackline Masters
Creating Line Plots Stage 2 Recording Sheet
Narrative
Students measure up to eight objects to the nearest quarter inch. They work with a partner to create a line plot to repre... |
8.F.B | Warm-up
This warm-up connects to the previous lesson and is meant to elicit ideas that will be helpful for students in the next activity in this lesson. Students should notice that the points in the graph are not connected and wonder how well the lines model the sections of data they span, which is explored further in ... |
8.F.A.1 | Problem 1
The tables below show some input and output values for two different functions.
Determine if each table represents a linear or nonlinear function.
a. Table A
###TABLE0###
b. Table B
###TABLE1###
Problem 2
Determine if each equation below represents a linear or nonlinear function. Be prepared to justify yo... |
F-IF.A.2 | Task
You put a yam in the oven. After 45 minutes, you take it out. Let $f(t)$ be the temperature of the yam $t$ minutes after you placed it in the oven.
In (a)–(d), explain the meaning of the statement in everyday language.
$f(0)=65$
$f(5) < f(10)$
$f(40)=f(45)$
$f(45) > f(60)$
|
G-SRT.B.5 | Activity
Because the angle of incidence of an object bouncing off another is equal to the angle of reflection, mirrors and pool tables make great contexts for using similar triangles. Billiards players really do estimate and measure similar triangles when setting up their trick shots, so this is a realistic context.
Al... |
3.NF.A.2 | Narrative
The purpose of this warm-up is for students to recognize that two values of reference are needed to determine the number that a point on the number line represents. The numbers 0 and 1 are commonly used when the numbers of interest are small. With only one number shown (for example, only a 0 or a 1), we can’t... |
S-CP.A.2 | Problem 1
Back to the diner!
You want to know if choosing cream or sugar are independent events, that is, if one depends on the other.
Below is a Venn diagram that represents the number of people in the diner one morning. A random person is chosen. Is this random person more likely to have cream in his coffee if he has... |
3.OA.A.1 | Problem 1
Pre-unit
Write a multiplication expression represented by each diagram.
###IMAGE0###
###IMAGE1###
|
G-MG.A | Task
A tessellation of the plane is an arrangement of polygons which cover the plane without gaps or overlapping. For example, part of a tessellation with rectangles is
pictured below:
###IMAGE0###
A tessellation is called
regular
if all polygons in the tessellation are congruent regular polygons and
if any two polyg... |
8.F.B.4 | Warm-up
The purpose of this warm-up is for students to reason about the values we can assign graphs based on which feature of the graph, such as slope and
\(y\)
-intercept, the viewer focuses on. Since there are no numbers on the graph, it is important for students to explain how they know the sign of the slope and
\(y... |
A-CED.A.3 | Problem 1
A step function is shown below.
###IMAGE0###
When does the function have a value of 4? Select all that apply.
$${f(4)}$$
$${f(5)}$$
$${f(7.99)}$$
$${f(8)}$$
$${f(8.01)}$$
Describe a situation that could be represented by this step function.
Problem 2
At the beginning of the week, Jessie had $500 in her bank a... |
6.EE.A.1 | Activity
In this activity, students apply the meaning of exponents to practice writing and evaluating exponential expressions. Students gain experience experimenting with equivalent numerical expressions and engage in looking for structure (MP7) when they replace a portion of an expression with something equivalent to ... |
7.RP.A.3 | Activity
In this activity, students match equations that represent a percent increase situation to the situations they represent.
Launch
Arrange students in groups of 2. 2 minutes of quiet think time followed by 2 minutes of partner discussion.
Student Facing
Match an equation to each of these situations. Be prepared t... |
7.SP.B.3 | Task
Below are the heights of the players on the University of Maryland women's basketball team for the 2012-2013 season and the heights of the players on the women's field hockey team for the 2012 season. (Accessed at http://www.umterps.com/sports/w-fieldh/mtt/md-w-fieldh-mtt.html, http://www.umterps.com/sports/w-bask... |
F-BF.A.1a | Warm-up
This opening warm-up gives students an opportunity to create a pictorial representation of exponential growth. The purpose of this warm-up is to help students make sense of the situation coming up in the next activity, where they are not explicitly asked to make a pictorial representation.
Student Facing
###IMA... |
7.G.B.4 | Optional activity
The purpose of this activity is for students to consider a different way to cut and reassemble a circle into something resembling a polygon in order to calculate its area. This time the polygon is a triangle, but the area of the circle can still be found by multiplying
\(\frac12\)
times the circumfere... |
3.OA.D.8 | Narrative
The purpose of this activity is to use students’ experience with multiplication and division within 100 to plan a school garden. In this activity, students make choices about which produce to grow. The choices are guided by some constraints, such as a desired yield. Students draw diagrams to represent how the... |
F-BF.A.1a | Activity
Building on their work in the warm-up, students make several compound-interest calculations in a credit card context. They revisit and explore how nominal and effective interest rates are used by credit institutions.
In a borrowing context, the nominal
annual percentage rate,
or the nominal APR, is 12 times th... |
1.OA.A.1 | Narrative
The purpose of this activity is for students to make sense of story problems that do not include a question. In some story types, like Add To, Change Unknown, students can infer what the question in the story is without it being asked. In problem types like Compare, there are multiple questions that can be an... |
G-GMD.A.1 | Task
The four diagonals of a cube with side length $\ell$ meet in a point $P$, and divide the cube into six rectangular pyramids with square bases.
What is the height of each of these pyramids?
What is the volume of each of these pyramids?
It seems reasonable to suppose that the volume of a rectangular pyramid is, like... |
8.G.C | Activity
The purpose of this activity is for students to learn or remember the names of the figures they worked with in the previous activity and learn a quick method for sketching a cylinder. Students start by determining the shapes that are the faces of the four shapes. They also determine which shape would be consid... |
1.NBT.A.1 | Stage 3: Estimate and Count Up to 120
Required Preparation
Materials to Gather
10-frames
Collections of objects
Cups
Paper plates
Materials to Copy
Blackline Masters
Counting Collections Stage 3 Recording Sheet
Narrative
Students are given a collection of up to 120 objects. They record an estimate for how many objects... |
F-BF.B.4 | Problem 1
Here is the graph of a function. What are the possible values for the domain for the inverse of this function?
###IMAGE0###
Problem 2
What is the domain that will make each of the following true functions?
$${f(x)=\sqrt{x-2}}$$
$${g(x)=2\sqrt{x}}$$
$${h(x)=\sqrt{x}+3}$$
$${ j(x)={{\sqrt{x}}\over{5}}}$$
$${k(x... |
7.RP.A.2 | Optional activity
The purpose of this activity is for students to write and solve equations as a strategy to compare the projected costs of using reusable versus disposable plates and forks. First, students examine dot plots representing the average number of customers served per day at a sample of restaurants to make ... |
5.MD.B.2 | Stage 4: Eighth Inches, Add, Subtract, and Multiply
Required Preparation
Materials to Gather
Objects of various lengths
Rulers (inches)
Materials to Copy
Blackline Masters
Creating Line Plots Stage 4 Recording Sheet
Narrative
Students measure up to eight objects to the nearest
\(\frac{1}{8}\)
inch. They work with a pa... |
8.EE.C.8a | Activity
In the previous lesson, students studied the set of solutions to a linear equation, the set of all values of
\(x\)
and
\(y\)
that make the linear equation true. They identified that this was a line in the coordinate plane. In this activity, they are given graphs of lines and then are asked whether or not diffe... |
6.EE.A.1 | Activity
This activity uses the context of a genie who gives a magic coin that doubles in number each day. This context reminds students about the need for exponential notation in thinking about problems involving repeated multiplication. For the sake of simplicity, the problem was written so that the exponent is equal... |
2.NBT.B.5 | Narrative
The purpose of this activity is to solve the story problems from the first activity. Monitor for the different ways students represent their thinking and solve their selected problems including:
tape diagrams to make sense of the problems
base-ten diagrams
equations
The goal of the activity synthesis is to sh... |
7.NS.A.1 | Warm-up
The purpose of this warm-up is to introduce students to a number line diagram they will be using to represent addition and subtraction of integers in future lessons. To introduce this idea, students write a story and equation that a given number line diagram could represent.
Launch
Tell students they are going ... |
F-IF.B.4 | Task
Mike likes to canoe. He can paddle 150 feet per minute. He is planning a river trip that will take him to a destination about 30,000 feet upstream (that is, against the current). The speed of the current will work against the speed that he can paddle.
Mike guesses that the current is flowing at a speed of 50 feet ... |
8.SP.A.4 | Activity
In this activity, students create two-way tables displaying relative frequency. The relative frequency table converts the actual frequency data to percentages which can be useful when comparing groups that include different totals. Finally, students use the relative frequencies to look for a pattern in the dat... |
7.RP.A.3 | Optional activity
This activity gives students an opportunity to practice various vocabulary terms that come along with percentages. Students are asked to sort scenarios to different descriptors using the images, sentences or questions found on the scenario cards. The questions found on the scenario cards are intended ... |
A-SSE.A.2 | Activity
This activity allows students to practice rewriting quadratic expressions in standard form by using the structure they observed in the earlier activity.
As students work, look for those who approach the work systematically: by looking for two factors of the constant term and that add up to the coefficient of t... |
3.MD.D.8 | Narrative
The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information.
Launch
Groups of 2
Display the image.
“What is an estimate that’s too high?” “Too low?” “About right?”
1 minute: quiet think time
Activity
“Discuss your thinking with ... |
6.G.A.1 | Warm-up
So far, students have determined area given a triangle and some measurements. In this warm-up, students are invited to reverse the process. They are given an area measure and are asked to create several triangles with that area.
Expect students to gravitate toward right triangles first (or to halve rectangles t... |
F-BF.A.2 | Warm-up
This is the first math talk activity in the course. See the launch for extended instructions for facilitating this activity successfully.
The purpose of this Math Talk is to elicit strategies and understandings students have for interpreting an exponential function and for multiplying fractions. These understan... |
1.MD.C.4 | Narrative
The purpose of this activity is for students to learn a new center activity called Sort and Display. This activity gives students an opportunity to sort items, represent how they sorted, and create questions that can be answered by their representation. Students sort items in any way they choose.
To connect t... |
F-TF.B.6 | Problem 1
Solve for the general solution:
$${3\mathrm{tan}^2x-3=0}$$
$${2\mathrm{cos}^2(x)-\sqrt3 \mathrm{cos}x=0}$$
$${2\mathrm{cos}^2x+\mathrm{cos}x-1=0}$$
Problem 2
Solve for the domain
$${0 \leq \theta \leq 2\pi}$$
:
$${2\mathrm{sin}^2\theta+\mathrm{cos}\theta\mathrm{sin}^2\theta=0}$$
|
F-LE.A.3 | Task
The table below shows the values of $2^x$ and $2x^3 + 1$
for some whole number values of $x$:
###TABLE0###
The numbers in the third column (values of $2x^3 + 1$) are all
larger than the numbers in the second column (values of $2^x$). Does this
remain true if the table is extended to include whole number values ... |
4.NF.B.3a | Narrative
This is a 5 Practices activity. Students use any strategy that makes sense to them to reason about subtraction of a fraction from a whole number. They begin by using an image to support their reasoning. Later, when no image is given, students may use a variety of ways to find differences. In the synthesis stu... |
5.OA.B.3 | Narrative
The purpose of this activity is for students to generate numerical patterns given two rules, form ordered pairs consisting of the corresponding terms, and graph the ordered pairs on the coordinate grid. The structure of the activity is the same as the previous activity but this time the multiplicative factor ... |
8.G.A.5 | Task
A common tiling pattern with hexagons is pictured below:
###IMAGE0###
A regular hexagon is a hexagon with $6$ congruent sides and $6$ congruent
interior angles. Find the measure of the interior angles in a regular hexagon.
Show that three equally sized regular hexagons sharing a common vertex can be arranged
in t... |
4.NBT.B.4 | Narrative
The purpose of this activity is for students to add and subtract multi-digit numbers through the hundred-thousands place. To find the value of some differences, students will decompose more than one unit.
The last question includes problems with a missing addend and a missing subtrahend. Besides making use of... |
6.SP.B.5c | Activity
In this activity, students measure the diameter and circumference of different circular objects and plot the data on a coordinate plane, recalling the structure of the first activity in this unit where they measured different parts of squares. Students use a graph in order to conjecture an important relationsh... |
G-MG.A.3 | Activity
In this activity, students are building skills that will help them in mathematical modeling (MP4). They formulate a model of a pizza slice as a sector of a circle. They compute unit costs per square inch of pizza to compare the value of several different vendors’ pizza deals. During the activity synthesis, stu... |
8.EE.B | Activity
The previous activity examined parallel lines and equations that define them, focusing on their common attributes (slope) and their different attributes (
\(y\)
-intercept). This activity further examines parallel lines, including situations where the
\(y\)
-intercept is negative. In addition, students match l... |
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