Eureka Math Lesson 3

In order to improve my instructional practices, I analyzed instructional data from district math diagnostic and proficiency assessments. The most recent assessment assessed student’s abilities to count, add and subtract, and their understanding of place value. My students scored below not only the other first grade students at the school, but also all first grade students in the district. 81.6% of my students could count, read, and write numbers to 120. This was an improvement from their diagnostic assessment. However, only 66.7% could relate counting to addition and subtraction, and only 45% demonstrated understanding of place value in two digit numbers.

The one to two more; one and two less concentrate the ideas of adding a number higher and one less than the given number. For example; if given the number 5, the number one more is 6, and less than 5 is 4. An activity to help promote mathematical students would allow them to use “six dot cards”. This could reinforce the idea and allow students to visually see the steps.

Students will use the words more or greater than, less than, same or equal to through and interactive text on numbers.

Students will develop understanding and strategies to solve addition and subtraction word problems with 20.

Today we will be learning about place value. When we divide numbers with three and four digits by a one digit number, the quotient doesn’t always go about the first number in the dividend like we saw yesterday. This is important to know because if you had to split $100 with your sister and you divided $100 by 2 and placed the 5 above the 1, then added two zeros, you would have to pay your sister $500. That’s not dividing, or fair. Remember we need to know how to divide so you can evenly split something, like money.”

Jazmine was introduced to two digit addition. My first lesson focused on drawing tens and ones to solve two digit addition. This strategy would provide Jazmine with the visuals she needs to solve the problem. First, I did a quick review on how to draw tens and ones to represent a number. She was given three examples ranging from easy to hard. Jazmine showed no signs of difficulty and was able to complete the task. Then, I demonstrated how to use the drawings to add two digit numbers. I explained how she must draw the picture for each addend. Then, I explained that she must count the tens first and then the ones. She smiled and said “that's easy”. We went through a couple of problems together and Jazmine displayed that she understood the strategy of drawing tens and ones to solve two digit

“So during this unit we have been working on adding numbers that equal greater than 10, and tomorrow we even started subtracting from numbers that are greater than ten. Before we continue on however, I want to teach you a little strategy on how to use a tens frame to help you solve problems.”

Understanding place value is integral to mathematics, and is especially for addition and subtraction. Being able to easily rearrange numbers between place values is required for most addition and subtraction problems. Part of grasping place value is being able to unitize. Fosnot and Dolk explain unitizing to be “a child’s construction of the logic to think of 10 flexibly as ten 1’s or as one unit of 10” (Taylor, Breck, & Aljets, 2004, p. 140). Unitizing is what makes “borrowing” in subtraction possible. If a problem is 32 – 16, one of the three tens must be broken up into units in order to subtract; being able to see 32 as 3 tens and 2 ones and as 2 tens and 12 ones is what makes the problem possible. Place value and unitizing have much to do with a comprehension of base ten, but they are not exclusive to base ten. For example, one could apply the idea of place value and unitizing to base five. The number 18510 would be written as 12205. The place values would then be 125, 25, 5, and 1 (instead of 1000, 100, 10, and 1), and 12205 would be understood as one 125, two 25s, and two 5s. Unitizing would allow for someone to

Montana demonstrated a number strategies and skills throughout the rational number interview. She used appropriate language when referring to fractions. For example, “two thirds” rather than “two over three” and she was able to divide 3 pizzas equally between 5 people using a partitioning method (cut/divided the 3 pizzas into 5 equal pieces and shared 1/5 a pizza 3 times between the 5 girls). She was also successful in identifying which decimal was larger when given a choice between two. For example, selected 0.87 being larger than 0.087 because ‘the number closest to the decimal point is larger – 8 is larger than 0’.

One of the key things that I learned from Developing Whole-Number Place-Value Concepts is that place value is an important concept for students to learn. This is so because students need to know the meaning of a number, especially when they are older. For example, when students are in 4th grade, they will need to know larger numbers, like 100,000. They will also need to know how to divide and multiple with larger numbers. So if students do not know the place value of these larger numbers, then they will not be able to understand important math concepts and operations. Thus, learning place value is important because everyone needs to understand the meaning of a number in order to do basic tasks and operations when they are older.

CC.2.1.2.B.1 Use place value concepts to represent amounts of tens and ones and to compare three digit numbers.

Multiplicative thinking, fractions and decimals are important aspects of mathematics required for a deep conceptual understanding. The following portfolio will discuss the key ideas of each and the strategies to enable positive teaching. It will highlight certain difficulties and misconceptions that children face and discuss resources and activities to help alleviate these. It will also acknowledge the connections between the areas of mathematics and discuss the need for succinct teaching instead of an isolated approach.

Multiplication by ten gives students opportunity to explore larger numbers, and can also be extended on(Reys et al. ch. 11.4). In addition, multiples of 10 give students the knowledge that all digits move left one place and an additional place hundreths. This concept can be used to introduce the decimal place which is also moving place each time something is multiplied by tens. Exposing students to a range of examples which displays patterns that occur when multiplying by tens and hundreths will generate meaning of digits moving place (Reys et al., ch. 11.4).

For most people who have ridden the roller coaster of primary education, subtracting twenty-three from seventy is a piece of cake. In fact, we probably work it out so quickly in our heads that we don’t consciously recognize the procedures that we are using to solve the problem. For us, subtraction seems like something that has been ingrained in our thinking since the first day of elementary school. Not surprisingly, numbers and subtraction and “carry over” were new to us at some point, just like everything else that we know today. For Gretchen, a first-grader trying to solve 70-23, subtraction doesn’t seem like a piece of cake as she verbalizes her confusion, getting different answers using

In this lesson, I am trying to accomplish teaching the students the key concepts of less than, greater than, and equal to. I want them to understand that each number holds its own value and that a specific number may hold