I reviewed the process of simplifying complex fractions with Samantha including expressions without variables. I then introduced equations with rational functions. I told Samantha that as soon as all rational functions had equal denominators, we could cancel them through the process of cross-multiplication. From that point, we could solve the remaining equation by linear or quadratic methods. There was no assignment.

Sam and I continued our study of the novel. Sam did a great job on her homework. We discussed her double journal entries first. We then continued reading the novel making sure to annotate for understanding and literary devices used for effect. We then worked on a few exercises in the vocabulary book. Sam does quite well with the application of the difficult vocabulary.

Discuss the main structure of hair being keratin. The structure of keratin as a fibrous, structural protein, insoluble in water and organic solvents. Keratin is also structurally found in nails, skin, and horns of many animals. Hair consists of 3 sections; the medulla or innermost part, the cortex , or middle highly structured part, and the cuticle,or outer layer containing lipids. The difference between the follicle, hair shaft and root bulb was summarized and diagrammed. Texture of hair consisting of curl pattern, volume, and consistency was discussed in detail for all 3. The shape of the follicle and the circumference determining the texture, volume, and consistency. The chemistry of hair lightening, using bleach to oxidize the melanin to colorless without changing the color of the keratin, which remains pale yellow. Hydrogen peroxide in alkaline solution is used, with the decomposition of peroxide to produce oxygen being the chemical reaction. The chemistry of permanent hair coloring, the use of ammonia to open the cuticle and the depositing of the color in the cortex was the final step in hair coloring.

The lesson outline was the same as Thursday's since Sam was absent for Thursday's. The anatomy and physiology of human hair was covered, specifically the major parts of the shaft being the medulla, cortex, and cuticle. The function of each part briefly discussed as to the location of the color pigments. The colors black and brown formed by the eumelanin and the red color formed by the pheomelanin. All other colors are blends of the pigments, dictated by genetics.

Samantha scored perfectly on her 8 homework questions that had her evaluate functions.
This was a topic that I had not reviewed with her, but she knew how to do it. Today I taught her how to multiply matrices. We can only do that when we have the following:
Matrix A is M x N and Matrix B is N x P. In other words, the number of columns in the first matrix must equal the number of rows in the second matrix. The resulting product will be a matrix of size M x P. I showed Sam several examples, and she then worked exercises 1-9 independently. Her homework is to complete # 10 & #11.

Sam and I had a lesson on annotating a text. We discussed the different levels of annotation. I modeled how you annotate a text. We read the novel stopping to discuss annotating. We also stopped to discuss the plot and characters. We briefly discussed Sam's next writing assignment which will be the Career Narrative. Sam needs to write three double journal entries for homework.

The anatomy of hair and the chemistry of hair will be discussed. The use of acidic dyes consisting of small pigment molecules that can slip inside the hair shaft as temporary hair color. The effect of peroxide on the shaft and how it allows shampoo to eventually dislodge the temporary color. The effect of ammonia, if used,will cause the shaft to open and damage natural color. The use of bleach to oxidize melanin and leave a pale yellow color along with peroxide which opens the shaft in alkaline solution to allow the reaction.

Student absent

Sam was absent today

Samantha and I worked on a few more problems in subtraction and addition of rational expressions and simplification of complex fractions. I guided her through problems where the denominators of the fractions involved had to be factored in various ways and the numerators had to be combined. There was no assignment.