I challenged Alexandra with different Kindergarten and first grade hands-on math activities. One involved composing shapes together with pattern blocks, another involved counting steps and then asking Alexandra to guess how many steps it would take to walk a certain distance - (how many steps will it take for you to go from your classroom to Ms. Judie's office)? I then let Alexandra count her steps to see if her guesses were accurate - and then see if her guess was higher or lower than the actual number of steps. We also cooked an imaginary pizza which I divided into four slices. Alexandra was to add her favorite toppings and add additional topping to 1 of the 4 slices (Alexandra chose pepperoni). This was an activity designed to integrate and synthesize Alexandra's preliminary understanding of parts of a whole - or fractions. When she ate her lunch, we used the compartments in her lunch box to figure out how many compartments of the whole were empty and how many were left after she finished the contents of her snack - green beans, cheese, and grapes. Next, we played a math bingo game. I created a Bingo board with numbers on from 1 -20 on it, and Alexandra had to add or subtract numbers and cover her board with counters after she she figured out the answers. Alexandra used the counter manipulatives and my fingers to count and then determine if that number was on the board. Alexandra grew excited when she created a diagonal line, solving the math problems, and getting BINGO! This activity was helpful in reinforcing basic addition and subtraction skills, and to improve her familiarity with math terms and help reinforce her understanding of patterns. Today was a fun way to help practice, reinforce, and consolidate her number sense skills in fun, hands-on ways.

Alexandra began today's session by working on an academic activity sheet called "cookie addition,' using pictures to add and write the sum in the spaces provided. The activity afforded an opportunity to use mathematical terminology (e.g., sum/equal) during computation. Alexandra used both my fingers and counters to assist her in performing the math required for successful outcome; we used concrete objects such as marbles, counters, blocks and other math manipulatives to assist in number correspondence activities. Prompts were afforded to facilitate her ability to write certain numbers. She holds a pencil correctly but had some difficulty remembering the exact order and orientation of certain numbers, such as the number 5 (this is known as mirror-writing, and is very common in young children, and often seen up to the age of 7). Alexandra was afforded practice via modeling to write the numbers 5 and 8, and we worked on handwriting and tracing activities to further strengthen her number perception and graphic ability to reproduce numbers. She clearly demonstrates an understanding of concepts of bigger than and less than and adding more and taking away. "If you have 3 apples and I don't take any away from you- how many will you have left??" "I'd have 3 apples." We've also begun working on broadening Alexandra's conceptual understanding of tens and ones and began writing two-digit numbers as I explained them as follows: after she counts objects (blue counters) to ten, she is asked to put them in a group and told it is a group of ten things. We then counted another group of counters, noting that it is another group of ten. We did this with three groups of ten, and Alexandra counted the 30 counters and I explained," there are three groups of ten. You just counted thirty blue counters in all. Now how do we count just 4 counters?" As she counts them, I explained that they are not in a group of ten, so they are in a group of ones; she wrote the number 4. I hope to teach expanded notation next to show Alexandra that there are 30 + 4 counters in the group and how to write the number 3 on the left and 4 for the numbers of ones. I verbally gave Alexandra a series of one and 2-digit numbers to write but she grew tired halfway through the activity, and prompting methods helped her complete the task. We also worked on repeating the pattern activity on which Alexandra completed half the assigned task. The activity used two and three different shapes in repetitive patterns. Alexandra understood how to complete the pattern, only having some difficulty reproducing multi-sided figures such as pentagons; however, she made a concerted effort to replicate them. I ended the session by drawing a picture of one of her unicorn stuffies and we readied ourselves for dismissal.

Decimal Operations, Conversion of Units. Multiplication and Division of Decimals, Word Poblems with Decimals. Conversion of Units : U.S Customary IP Units: Volume, Length and Mass unit conversion problems.

Alexandra began working on an exercise involving shapes. It required that she count the sides of the shapes and color according to a key provided. She was reminded of the names of the shapes and encouraged to repeat them and subsequently queried for recall. She also was tasked with filling in the blanks about 2 dimensional objects and their surfaces (flat or curved). Alexandra was exposed to a variety of hands-on activities that involved tracing, drawing, naming, and identifying 2D shapes and comparing them to real life objects, (e.g., a shoebox, a spoon, a pan), which further developed Alexandra's ability to recognize the difference between 2D and 3D shapes and discuss their characteristics, such as the numbers of corners and sides. Alexandra was also presented with word problems tasking her with using check marks on pictorial graphs to solve problems. Math vocabulary such as "how many pieces of fruit did she buy in all?" was reinforced. Finally, Alexandra used a color code to color the picture which developed concepts of greater than and less than ("what number is greater than 8 but less than 10') to further develop, reinforce and refine her number sense.

Emilia's familiarity to the foundational concepts of grouping and sharing was reinforced and she was shown examples of how creating equal groups relates to multiplication. I reinforced the idea of repeated addition, such as grouping sets of two or three to understand concepts like 2+2+2=6. Division is introduced to share objects equally among groups. An example would be to divide ten apples among five kids to understand that each child gets 2 apples - or the one used today was to share a pizza pie divided into quarters so that each of two children can receive two slices each. Visual aids, manipulatives, story problems, and real-world scenarios were used to reinforce these concepts. Emilia received additional practice to add and subtract and learn about the relationship between addition and subtraction using fact families. Emilia continues to receive encouragement to apply mental math strategies and simple problems for contextual understanding. For the problem, '8+5,' Emilia can choose to use a number line to start at 8 and move 5 spaces to reach 13. For '14-6,' she may use counters, starting at 14 and removing 6 to see the remainder. These activities and strategy options engage her and build familiarity with numbers and their relationships.

Computation/math concepts

We began by reading a book about the shape of things to reinforce the concept that shapes make up the world around us. The book contained simple rhymes and illustrations to help illustrate the idea to be able to distinguish the shapes in nature and the environment. One example we discussed and drew began with a diamond shape, which we transformed into a kite when we added some string - or a tail to it. Alexandra was encouraged to manipulate, draw, compare, describe, sort, and represent shapes in a variety of ways in order to develop and concretize ideas about shapes. We expanded this concept by working on exercises which included a discussion of geometric shapes using math vocabulary. Alexandra was prompted to describe shapes and other objects using relationship words like, 'near, 'under, 'by,' on top of,' below,' 'right,' and 'left.' I also introduced Alexandra to another book which challenged her to count and distinguish shapes up to 50. We continued reading another book that tasked Alexandra with skip counting by 2's 5's and 10's. We used an abacus to show different ways to show and represent numbers and Alexandra worked independently on an exercise in which she looked at objects and then drew a circle around the solid figure on the line next to it that looked like its shape. She was also tasked with naming it. To stimulate higher-order thinking, Alexandra was prompted to name the solid figure shown and to then draw two additional objects that looked like that shape. She showed a very good understanding and execution of tasks given to her.

Emelia and i continued to address foundational number sense and basic operations. I presented Emelia with various problems to facilitate her familiarity and performing addition and subtraction, including word problems. I introduced fun activities and manipulatives (e.g., 10 blocks) to introduce a real-world experience to her number sense and engagement. She also was tasked with comparing numbers to help refine her ability to determine which of two numbers is greater, less than, or equal to. She was also introduced to a bar graph and answered questions requiring her to use both addition and subtraction processes to figure out the answers. Emelia remains an active and engaged participant in activities and work assigned to her, and she and is responsive to interventions and to strategies suggested to broaden her scope and understanding of number analysis. She enjoyed working with Magna Tiles to create 3 dimensional shapes and structures. She finished our session skip counting by twos, fives and tens to 100.

Today, we continued to focus on foundational number sense and basic operations. This included counting to 100, skip counting, recognizing and writing numbers, comparing numbers, solving simple addition and subtraction problems within 10, and identifying basic geometric shapes. Alexandra worked on a cut-and-paste activity to identify different sized figures and was introduced to academic subject-specific vocabulary pertaining to shapes ((e.g., hexagon and octagon). As promised, I brought in additional connect-the-dot exercises and she completed three of them, receiving stickers for her finished work. The use of hands-on activities and manipulatives facilitated and helped foster development and refinement of recently acquired skills.

Alexandra worked on several skills this afternoon. She began with a tracing activity and demonstrated excellent fine motor control and fine-finger dexterity using a pencil; she prefers a short pencil as she has greater control with it. I introduced word problems in this session and Alexandra was permitted to work with manipulatives to arrive at the answers. I introduced additional terminology that offered clues as to whether addition or subtraction was the strategy to use in each problem. For other math exercises, we used dominoes and Alexandra counted the dimples on the tiles to arrive at answers to the addition problems. She enjoyed receiving sparkly stickers for task completion and following directions promptly. During her break, Alexandra clearly enjoyed assembling a marble run with her sister and both guessed which trajectory the marbles would follow depending on how the connecting pipes were configured. Alexandra joined her sister for the last five minutes of class and they both took turns on an educational game which incorporated several of the skills acquired in class and called on the execution of higher order cognition to achieve successful outcomes.