my homework lesson 3 sequences

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McGraw Hill My Math Grade 4 Chapter 7 Lesson 3 Answer Key Sequences

All the solutions provided in McGraw Hill Math Grade 4 Answer Key PDF Chapter 7 Lesson 3 Sequences  will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 4 Answer Key Chapter 7 Lesson 3 Sequences

Explanation: Number of pages on the first day she reads = 25. Number of pages each day she reads = 25. Number of pages each day she reads on Monday = Number of pages on the first day she reads = 25. Number of pages each day she reads on Tuesday = Number of pages each day she reads on Monday + Number of pages each day she reads = 25 + 25 = 50. Number of pages each day she reads on Wednesday = Number of pages each day she reads on Tuesday + Number of pages each day she reads = 50 + 25 = 75. Number of pages each day she reads on Thursday = Number of pages each day she reads on Wednesday + Number of pages each day she reads = 75 + 25 = 100. Number of pages each day she reads on Friday = Number of pages each day she reads on Thursday + Number of pages each day she reads = 100 + 25 = 125.

Explanation: The first term of a sequence is 65. The rule of the sequence is subtract 4. Next four terms in the sequence: 61 – 4 = 57. 57 – 4 = 53. 53 – 4 = 49. 49 – 4 = 45. Next Six terms in the sequence: 45 – 4 = 41. 41 – 4 = 37. 37 – 4 = 33. 33 – 4 = 29. 29 – 4 = 25. 25 – 4 = 21. The pattern to a total of 10 terms: 65, 57, 53, 49, 45, 41, 37, 33, 29, 25, 21. Another observation about the pattern: The ones digits repeat the pattern 5, 1, 7, 3, and 9.

Answer: The operation of a rule affect the terms of a sequence as it helps to find any term in the problem.

Explanation: An operation is a mathematical action. Addition, subtraction, multiplication, division, and calculating the root are all examples of a mathematical operation

Guided Practice Extend each pattern by four terms. Write an observation about the pattern. Question 1. Rule: add 7 Pattern: 8, ___, ___, ___, ___ Observation: ________ Answer: Pattern: 8, 15, 22, 29, 36. Observation: It is observed that four numbers are prime and 1 is composite number.

Explanation: Rule: add 7 8 + 7 = 15. 15 + 7 = 22. 22 + 7 = 29. 29 + 7 = 36. Pattern: 8, 15, 22, 29, 36.

Question 2. Rule: subtract 10 Pattern: 90, ___, ___, ___, ____ Observation: __________ Answer: Pattern: 90, 80, 70, 60, 50. Observation: It is observed the numbers are Multiplies of 10.

Explanation: Rule: subtract 10 90 – 10 = 80. 80 – 10 = 70. 70 – 10 = 60. 60 – 10 = 50. Pattern: 90, 80, 70, 60, 50.

McGraw Hill My Math Grade 4 Chapter 7 Lesson 3 My Homework Answer Key Practice

Extend each pattern by four terms. Write an observation about the pattern. Question 1. Rule: add 8 Pattern: 5, ___, ___, ___, ____ Observation: ________ Answer: Pattern: 5, 13, 21, 29, 37. Observation: It is observed all numbers are prime numbers.

Explanation: Rule: add 8 5 + 8 = 13. 13 + 8 = 21. 21 + 8 = 29. 29 + 8 = 37. Pattern: 5, 13, 21, 29, 37.

Question 2. Rule: multiply by 2 Pattern: 3, ___, ___, ___, ____ Observation: __________ Answer: Pattern: 3, 6, 12, 24, 48. Observation: It is observed all numbers are even numbers.

Explanation: Rule: multiply by 2 3 × 2 = 6. 6 × 2 = 12. 12 × 2 = 24. 24 × 2 = 48.

Question 3. Rule: subtract 20 Pattern: 175, ___, ___, ____ Observation: ________ Answer: Pattern: 175, 155, 135, 115, 95. Observation: It is observed all numbers are multiplies of 5.

Explanation: Rule: subtract 20 175 – 20 = 155. 155 – 20 = 135. 135 – 20 = 115. 115 – 20 = 95.

Question 4. Extend the pattern below by four terms. Write an observation about the pattern. Rule: multiply by 10 Pattern: 26, ___, ___, ____, ____ Observation: ___________ Answer: Pattern: 26, 260, 2600, 26000, 260000. Observation: It is observed all numbers are even and are increasing.

Explanation: Rule: multiply by 10 26 × 10 = 260. 260 × 10 = 2,600. 2,600 × 10 = 26,000. 26,000 × 10 = 2,60,000.

Problem Solving Question 5. Mathematical PRACTICE 8 Look for a Pattern Brad puts an equal amount of money in his savings account once a month. He started with $25. The next month, he had $35 in his account. Two months after that, he had $55 in his account. How much money will Brad have in his account after 6 months? Describe a rule. Then solve. Answer: Amount of savings the next six months he had in his account = $175.

Explanation: Amount of savings he started = $25. Amount of savings the next month he had in his account = $35 . Amount of savings on three months he had in his account = $55. Amount of savings in a month he did = Amount of savings the next month he had in his account – Amount of savings he started = $35 – $25 = $10. Amount of savings the next three months he had in his account = Amount of savings in two month he did + (Number of months + Number of months) = $35 + (2 × Amount of savings in a month he did) = $35 + (2 × $10) = $35 + $20 = $55. Amount of savings the next four months he had in his account = Amount of savings in three months he did + (Number of months + Amount of savings in a month he did) = $55 + (3 × $10) = $55 + $30 = $85. Amount of savings the next five months he had in his account = Amount of savings in four months he did + (Number of months + Amount of savings in a month he did) = $85 + (4 × $10) = $85 + $40 = $125. Amount of savings the next six months he had in his account = Amount of savings in five months he did + (Number of months + Amount of savings in a month he did) = $125 + (5 × $10) = $125 + $50 = $175.

Question 6. On Monday, a toy store sold 4 race cars. On Tuesday, it sold 8 race cars. On Wednesday, it sold 16 race cars. . Suppose this pattern continues. How many race cars will be sold on Friday? Describe a rule. Then solve. Answer: Number of race cars a toy store sold on Friday = 64.

Explanation: Number of race cars a toy store sold on Monday = 4. Number of race cars a toy store sold on Tuesday = 8. Number of race cars a toy store sold on Wednesday = 16 Number of race cars a toy store sold on Thursday = Number of race cars a toy store sold on Wednesday  × 2 = 16 × 2 = 32. Number of race cars a toy store sold on Friday = Number of race cars a toy store sold on Thursday × 2 = 32 × 2 = 64.

Vocabulary Check Write a vocabulary word to complete each sentence. sequence term

Question 7. Each number in a numeric pattern is a ____ Answer: Each number in a numeric pattern is a term.

Explanation: A term is a single mathematical expression. It may be a single number (positive or negative), a single variable ( a letter ), several variables multiplied but never added or subtracted. Some terms contain variables with a number in front of them.

Question 8. A ____ is the ordered arrangement of terms that make up a pattern. Answer: A sequence is the ordered arrangement of terms that make up a pattern.

Explanation: A Sequence is a list of things (usually numbers) that are in order.

Test Practice Question 9. Identify the next term in the sequence. 171, 141, 111, 81, ____ A. 61 B. 51 C. 41 D. 31 Answer: 51 is the next term in the sequence. B. 51.

Explanation: Sequence: 171, 141, 111, 81, ?? 171 – 141 = 30. 141 – 111 = 30. 111 – 81 = 30. 81 – 30 = 51.

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Sequences Homework

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Sequences Homework Good in class as a handout for consolidation ; working together in groups during whole class teaching or for independent homework.

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Sum of an Arithmetic Sequence (Lesson 1.3)

Unit 1: sequences and linear functions, day 1: recursive sequences, day 2: applications of arithmetic sequences, day 3: sum of an arithmetic sequence, day 4: applications of geometric sequences, day 5: sequences review, day 6: quiz 1.1 to 1.4, day 7: linear relationships, day 8: point-slope form of a line, day 9: standard form of a linear equation, day 10: quiz 1.5 to 1.7, day 11: unit 1 review, day 12: unit 1 test, unit 2: linear systems, day 1: linear systems, day 2: number of solutions, day 3: elimination, day 4: larger systems of equations, day 5: quiz 2.1 to 2.4, day 6: systems of inequalities, day 7: optimization using systems of inequalities, day 8: quiz 2.5 to 2.6, day 9: unit 2 review, day 10: unit 2 test, unit 3: function families and transformations, day 1: interpreting graphs, day 2: what is a function, day 3: translating functions, day 4: quiz 3.1 to 3.3, day 5: quadratic functions and translations, day 6: square root functions and reflections, day 7: absolute value functions and dilations, day 8: equations of circles, day 9: quiz 3.4 to 3.7, day 10: unit 3 review, day 11: unit 3 test, unit 4: working with functions, day 1: using multiple strategies to solve equations, day 2: solving equations, day 3: solving nonlinear systems, day 4: quiz 4.1 to 4.3, day 5: combining functions, day 6: composition of functions, day 7: inverse relationships, day 8: graphs of inverses, day 9: quiz 4.4 to 4.7, day 10: unit 4 review, day 11: unit 4 test, unit 5: exponential functions and logarithms, day 1: writing exponential functions, day 2: graphs of exponential functions, day 3: applications of exponential functions, day 4: quiz 5.1 to 5.3, day 5: building exponential models, day 6: logarithms, day 7: graphs of logarithmic functions, day 8: quiz 5.4 to 5.6, day 9: unit 5 review, day 10: unit 5 test, unit 6: quadratics, day 1: forms of quadratic equations, day 2: writing equations for quadratic functions, day 3: factoring quadratics, day 4: factoring quadratics. part 2., day 5: solving using the zero product property, day 6: quiz 6.1 to 6.4, day 7: completing the square, day 8: completing the square for circles, day 9: quadratic formula, day 10: complex numbers, day 11: the discriminant and types of solutions, day 12: quiz 6.5 to 6.9, day 13: unit 6 review, day 14: unit 6 test, unit 7: higher degree functions, day 1: what is a polynomial, day 2: forms of polynomial equations, day 3: polynomial function behavior, day 4: repeating zeros, day 5: quiz 7.1 to 7.4, day 6: multiplying and dividing polynomials, day 7: factoring polynomials, day 8: solving polynomials, day 9: quiz 7.5 to 7.7, day 10: unit 7 review, day 11: unit 7 test, unit 8: rational functions, day 1: intro to rational functions, day 2: graphs of rational functions, day 3: key features of graphs of rational functions, day 4: quiz 8.1 to 8.3, day 5: adding and subtracting rational functions, day 6: multiplying and dividing rational functions, day 7: solving rational functions, day 8: quiz 8.4 to 8.6, day 9: unit 8 review, day 10: unit 8 test, unit 9: trigonometry, day 1: right triangle trigonometry, day 2: solving for missing sides using trig ratios, day 3: inverse trig functions for missing angles, day 4: quiz 9.1 to 9.3, day 5: special right triangles, day 6: angles on the coordinate plane, day 7: the unit circle, day 8: quiz 9.4 to 9.6, day 9: radians, day 10: radians and the unit circle, day 11: arc length and area of a sector, day 12: quiz 9.7 to 9.9, day 13: unit 9 review, day 14: unit 9 test, learning targets.

Find the sum of an arithmetic sequence with a set number of terms.

Interpret summation notation and calculate the sum.

Activity: The Super Stairs

Lesson handouts, media locked.

Our Teaching Philosophy:

Experience first, formalize later (effl), experience first.

The goal of today's lesson is for students to create a formula for the partial sum of an arithmetic sequence. That is a lofty goal! You might be thinking, "There's no way you can EFFL this lesson." But guess what, you can! It might take a little more teacher guidance than other lessons, but still, students can come up with the formula without you telling it to them. It will be very tempting to just tell them the formula when they get stuck, but trust the process! Today's lesson is an adaptation of a lesson created by Dan Meyer , called The Super Stairs. To start, show this video to the class. After that, let students take off! They should be able to work through questions #1-3 pretty quickly. Things start getting tough around #4. Here's where you will want to have your guiding questions all queued up.

Guiding Questions:

• Tell me about how you found the number of steps for 3 stairs. How did you find it for 8 stairs?
• Do you notice any patterns for the number of steps it takes for 8 stairs?
• How did you calculate your answer for 8 stairs? Did you use a calculator or do it in your head? Are there any shortcuts?

A goal during this time is to get students to notice that when they were adding up 2 + 4 + ... + 14 + 16 for the 8 stairs, they could pair the terms so that each pair equals 18. The first and last terms (2 + 16 = 18) show us what the sum of the pairs should be. Since we're pairing, we take the number of terms and divide it by two to find the number of pairs. This would leave them with 4 pairs of 18. They can use this idea to find the pairs for a staircase with 21 stairs.

Another way students can approach this problem is by adding the sequence twice to see the pairs. To get students thinking about this I tell them, "When I do the Super Stairs, I like to start with stair 21 first and work my way down. What would my sequence look like? Write it under the sequence you listed out for Dan. What do you notice? What if you added my sequence with Dan's sequence?" This method requires a bit more teacher guidance but I like to show how either way, we end up with the same total.

Formalize Later

When most groups have completed the front page, it's time to debrief. You'll want to make sure you point out that we are adding an arithmetic sequence. Have students explain their work to the class and how they came up with their total number of steps. If groups solved the problem in a different way, make sure to highlight the variety of different approaches. As a class, talk through how to write a formula for the total number of steps using terms like "first", "last", and "# of steps". Try to keep this all in the context of the problem for question #4. But once you've done that, you can swap in the algebraic version for question #5. And voila, your kids just came up with the formula for the partial sum of an arithmetic sequence!

Note: Here is a video showing the solution to the number of steps that it takes Dan to complete the 21 stair Super Stairs.

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Unit 4 – Linear Functions and Arithmetic Sequences

This unit is all about understanding linear functions and using them to model real world scenarios.  Fluency in interpreting the parameters of linear functions is emphasized as well as setting up linear functions to model a variety of situations. Linear inequalities are also taught. The unit ends with a introduction to sequences with an emphasis on arithmetic.

Proportional Relationships

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Unit Conversions

Nonproportional Linear Relationships

More Work Graphing Linear Functions

Writing Equations in Slope-Intercept Form

Modeling with Linear Functions

More Linear Modeling

Strange Lines – Vertical and Horizontal

Absolute Value and Step Functions

The Truth About Graphs

Graphs of Linear Inequalities

Introduction to Sequences

Arithmetic Sequences

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Unit #4 Review – Linear Functions and Arithmetic Sequences

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U04.AO.03 – Lesson #9.5 – Absolute Value Equations

U04.AO.04 – Turning Patterns into Sequences (after Lesson #13) – Enrichment Lesson

U04.AO.05 – Linear Modeling of Population (Extended Problem)

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What is Lesson Sequencing and How Can it Save You Time?

Author: Ben Greenwood

Posted: 03 Oct 2019

Estimated time to read: 3 mins

Lesson planning is a crucial part of PPA (Planning Preparation and Assessment), it can be the difference between a successful lesson and a complete classroom catastrophe. Ensuring that teachers have access to tried and tested marking techniques can reduce workload and improve teachers’ mental health, as well as maximising students’ academic progress.  

What is Lesson Sequencing?

Lesson sequencing is a holistic approach to lesson planning. It clusters lessons together to make transitions between them as smooth and simple as possible. Lesson sequencing uses the ‘Learning Arc’ concept to create a plan that gives students exactly what they need to learn effectively at different stages of the learning process. 

The Learning Arc

Lesson Sequence Plan

The main steps to creating a lesson sequence plan

• Decide on a sequence objective 

Choose an overall objective to get your students from the beginning to the end of the learning arc. The objective of each lesson will be to get one step closer to this sequence objective.

• Determine how a sequence can progress the class along the learning arc

What do students need to progress to the sequence objective and how can you get them there? Make note of all aspects of the topic that they need to learn.  

• Break this sequence down into manageable chunks

Once you’ve set out everything along the learning arc, break the information down into smaller chunks to set the outline for each of your lessons. 

• Ensure each chunk fits into a lesson and an accompanying h/w task

You might have to do some regrouping, but once you’ve broken the sequence down, you’ll get a good idea of what you need to teach in each lesson.

• Create your individual lessons 

Using the sequence as a guide, build out each lesson with its own objective and supporting resources, as well as a valuable homework task to either consolidate on the lesson previous or prepare for the upcoming lesson. (For help with this, download our sequencing lesson plan template below).

What makes a good lesson? 

A good lesson is one that simultaneously engages, challenges and supports students in their journey from the beginning of the learning arc to the end. It ensures that all students are where they need to be and know what they need to do to progress. A good lesson plan also takes into account the needs of SEND (Special Educational Needs and Disabilities) students and will have a section for differentiated work so that the whole class is able to progress at the right pace.

This is made easier by planning in a sequence, rather than lesson by lesson, as sequences tend to set SEND support protocol, possible extension work and differentiated work for the entirety of the sequence, this helps to ensure consistency in lessons, putting students at ease. 

How can SLT facilitate outstanding lesson sequencing that saves time? 

Giving teachers the time they need to properly conduct PPA is vital. The government’s School Teachers Pay and Conditions Document stipulates that teachers must be given at least 10% of their workweek set aside for guaranteed PPA, within their directed time of 195 days or 1,265 work hours. This ensures that teachers have time to create lessons within the school day that are engaging, useful and a vehicle for getting students from the beginning of the learning arc to the end of it. 

In order to facilitate outstanding lesson planning, SLT should seek to provide helpful content like a lesson plan template and possible assessment strategies that aid better workload management and help staff to cut down on planning hours. By confronting the workload crisis head on and safeguarding teachers’ mental health and time, not only will schools see happier, less stressed staff, they will also see more engaged, higher achieving students.

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