Learning Trajectories Discussion # 4

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Addition: Early Addition, Subtraction, and Counting Strategies

After reading chapter 5, closely look at Table 5.1 and 5.2: A Learning Trajectory for Addition and Subtraction.

Each student will examine two age groups. For these two age groups:

1. summarize the developmental progression and
2. give an example of one instructional task for each developmental level.

Your age group will be determined by your last name. It will change this week so check and see your new age group.

• For students with a last name starting with A-H  look at ages 5 and 6
• For students with a last name starting with I-0 look at ages 7 and 8
• For students with a last name starting with P-Z look at ages 3 and 4

Respond to a classmate who discussed a different age. What did you learn from them?

Link to textbook my last name starts with c

https://drive.google.com/file/d/1FEs0AiHjhWshQbeejUQ7Xx7l31xbAuII/view?usp=drivesdk

Respond to  post below Joshua

Age 3

1. The developmental progression for a 3-year-old is nonverbal +/- Adds and subtracts very small collections nonverbally. A child at this age should be able to show 2 objects than 1 object going under a napkin, and identifies or makes a set of 3 objects to “match.”
2. Solving nonverbal “join, result unknown” or “separate, result unknown” (take away) using the smallest numbers: For example, children are shown 2 objects than 1 object going under a napkin and then asked to show how many. Pizza Pizzazz 4: Students add and subtract numbers up to totals of 3 (with objects shown, but then hidden), matching target amounts.

Age 4

1. The developmental progression for a 4-year-old is small Number +/- Finds sums for joining problems up to 3 + 2 by “counting all” with objects. When a child in this age group is asked, “You have 2 balls and get 1 more. How many in all?,” count out 2, then count out 1 more, then counts all 3: “1, 2, 3 … 3!”
2. Instructional task for this developmental progression is Finger Word Problems: Challenge children to solve simple addition problems with their fingers. Use very small numbers. Children should place their hands on their laps between each problem.

Learning Trajectories Discussion # 4

1717 unread replies.2828 replies.

Addition: Early Addition, Subtraction, and Counting Strategies

After reading chapter 5, closely look at Table 5.1 and 5.2: A Learning Trajectory for Addition and Subtraction.

Each student will examine two age groups. For these two age groups:

1. summarize the developmental progression and
2. give an example of one instructional task for each developmental level.

Your age group will be determined by your last name. It will change this week so check and see your new age group.

• For students with a last name starting with A-H  look at ages 5 and 6
• For students with a last name starting with I-0 look at ages 7 and 8
• For students with a last name starting with P-Z look at ages 3 and 4

Respond to a classmate who discussed a different age. What did you learn from them?

Last name c

Respond to classmate Kelley

• summarize the developmental progression

At the age of three students nonverbally add and subtract very small collections. When presented with two objects and one going under a napkin the student makes a set of 3 objects to match it nonverbally. At the age of 4 the student will find sums oof conjoining numbers up to 3 +2 doing so by “counting all” with objects. When asked ” you have 2 balls and get 1 more. How many in all?” counts out 2, then counts out 1 more, then counts all 3: “1, 2, 3…3!

2. give an example of one instructional task for each developmental level.

One instructional task for a 3 year old is solving nonverbal “join, result unknown” or “separate , result unknown” using the smallest numbers.  A child is shown two objects then one object going under a napkin and then asked to say how many objects. One instructional task for a 4 year old is word problems. Tell the children o solve simple addition problems with toys that represent the objects in the problems. Totals up to 5. Tell the student that you want to buy three girl dolls and two boy dolls. Ask how many dolls that is all together.

Shyane Jones

Shyane Jones

Jul 6, 2022Jul 6 at 3:59pm

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Kelly

Great post! I learned that at age 3 students nonverbally add and subtract very small collections. I enjoyed reading about the instructional task parallel to this developmental progression. I think that it is so fascinating the way the mind of a child works!

Kayla Daly

Kayla Daly

FridayJul 8 at 9:37pm

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Hi Kelly, Great post I was able to see how a 3 year old progresses with adding numbers through 4 years old. I liked the instructional task for a 4 year old to learn adding numbers which is word problems. At first I thought this was a little to advanced but after reading the example it makes sense they would learn this way because it could be a scenario more relatable to them rather than just seeing numbers that they can’t relate to at all.

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Collapse SubdiscussionJohanna Pedone

Johanna Pedone

Jul 3, 2022Jul 3 at 12:16pm

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Age 3

1. The developmental progression for a 3-year-old is nonverbal +/- Adds and subtracts very small collections nonverbally. A child at this age should be able to show 2 objects than 1 object going under a napkin, and identifies or makes a set of 3 objects to “match.”
2. Solving nonverbal “join, result unknown” or “separate, result unknown” (take away) using the smallest numbers: For example, children are shown 2 objects than 1 object going under a napkin and then asked to show how many. Pizza Pizzazz 4: Students add and subtract numbers up to totals of 3 (with objects shown, but then hidden), matching target amounts.

Age 4

1. The developmental progression for a 4-year-old is small Number +/- Finds sums for joining problems up to 3 + 2 by “counting all” with objects. When a child in this age group is asked, “You have 2 balls and get 1 more. How many in all?,” count out 2, then count out 1 more, then counts all 3: “1, 2, 3 … 3!”
2. Instructional task for this developmental progression is Finger Word Problems: Challenge children to solve simple addition problems with their fingers. Use very small numbers. Children should place their hands on their laps between each problem.

Learning Trajectories Discussion # 5

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Composition, Place Value, and Multi-digit Arithmetic

After reading chapter 6, closely look at Table 6.3: A Learning Trajectory for composition, place value, and multi-digit arithmetic

Each student will examine two age groups. For these two age groups:

1. summarize the developmental progression and
2. give an example of one instructional task for each developmental level.

Your age group will be determined by your last name. It will change this week so check and see your new age group.

• For students with a last name starting with A-H  look at ages 7 and 8
• For students with a last name starting with I-0 look at ages 3 and 4
• For students with a last name starting with P-Z look at ages 5 and 6

Respond to a classmate who discussed a different age. What did you learn from them?

• Seven Nicole

1. A 7 year old should be able to solve all types of problems with flexible strategies and known combinations. Multidigit may be solved by incrementing or combining tens and ones (latter not used for join, change unknown.) For example: “Whats 28+35?” Incrementer thinks: 20+30=50; +8=58; 2 more is 60, 3 more is 63

2. One activity for a 7 year old would be Adding and subtracting tens with the empty number line. You would present addition problems under an empty number line and have students talk aloud to solve the problem, representing their thinking on the empty number line.

Eight

1. An 8 year old should be able to use composition of 10s and all previous strategies to solve multi digit +/- problems. For example: Ask “Whats 37-18?” and they say “I take 1 ten off the 3 tens; that 2 tens. I take 7 off the 7. That’s 2 tens and zero…20. I have one more to take off. That’s 19.”
2. One activity for an 8 year old would be Jumping to 100. You would use numeral cubes, one with numerals 1 to 6 and other with 10,20,30,10,20,30, two teams take turns throwing the cubes and, starting at 0, add that number to their position on an empty number line. Whoever reaches or passes 100 first wins.

Shyane Jones

Shyane Jones

SaturdayJul 9 at 6:03pm

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Nicole,

Great post! I really enjoyed learning about the instructional post that goes parallel with the developmental progression for a 7 year old. The empty number line is a GREAT idea and it will help really show how much of the content the 7 year old truly does understand!

Allison Padula

Allison Padula

SundayJul 10 at 12:39am

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Hi Nicole! From your post I was able to learn that at the ages of 7 and 8 is when children begin to really be challenged on what they know. Throughout all ages the children learn something new and carry it with them to their next lesson. I like the example of the game of Jumping to 100. This game encourages the children to use what they’ve learned and has some friendly competition involved. In addition, this game has no rhyme or reason to it. This shows that the children aren’t learning to memorize a pattern but memorize the concept being taught.

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Collapse SubdiscussionShyane Jones

Shyane Jones

SaturdayJul 9 at 6:01pm

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A developmental progression for ages 3-4 would be for a children to know that a whole is bigger than parts, but may not accurately quantify.

An instruction task for ages 3-4 would be experience in learning trajectories from previous chapters, which are appropriate in developing the developmental progression. So such content might include, subtilizing, counting, comparing and sorting.