Summarize the following:
The distributive property states that a(b+c)=ab+ac{\displaystyle a(b+c)=ab+ac}. This rule allows you to cancel out parentheses by multiplying each term in the parentheses by the number outside the parentheses. For example, if your equation is 2(10−2x)=4(2x+2){\displaystyle 2(10-2x)=4(2x+2)}, use the distributive property to multiply the terms in parentheses by the number outside the parentheses:2(10−2x)=4(2x+2){\displaystyle 2(10-2x)=4(2x+2)}20−4x=8x+8{\displaystyle 20-4x=8x+8} To cancel the variable, complete the opposite operation as stated in the equation. For example, if the term is subtracted in the equation, cancel it by adding. If the term is added in the equation, cancel it by subtracting. It is usually easiest to cancel the variable with the smaller coefficient. For example, in the equation 20−4x=8x+8{\displaystyle 20-4x=8x+8}, cancel the term −4x{\displaystyle -4x} by adding 4x{\displaystyle 4x}:20−4x+4x=8x+8{\displaystyle 20-4x+4x=8x+8}. Whatever you do to one side of the equation, you must do to the other side as well. So if you add or subtract to cancel the variable on one side of the equation, you must add or subtract to the other side as well. For example, if you added 4x{\displaystyle 4x} on one side of the equation to cancel the variable, you must also add 4x{\displaystyle 4x} to the other side of the equation:20−4x+4x=8x+8+4x{\displaystyle 20-4x+4x=8x+8+4x} You should now have the variable on one side of the equation. For example:20−4x+4x=8x+8+4x{\displaystyle 20-4x+4x=8x+8+4x}20=12x+8{\displaystyle 20=12x+8} You want the variable term on one side, and the constant on the other side. To move the constant to one side, add or subtract from each side of the equation to cancel the term on one side. For example, to cancel the +8{\displaystyle +8} constant on the variable side, subtract 8 from both sides of the equation:20=12x+8{\displaystyle 20=12x+8}20−8=12x+8−8{\displaystyle 20-8=12x+8-8}12=12x{\displaystyle 12=12x} To do this, perform the operation opposite from the one denoted in the equation. Usually this will mean dividing to cancel a coefficient being multiplied by a variable. Remember that whatever you do to one side of the equation, you must do to the other side of the equation as well. For example, to cancel out the coefficient 12 from the equation, you would divide each side of the equation by 12:12=12x{\displaystyle 12=12x}1212=12x12{\displaystyle {\frac {12}{12}}={\frac {12x}{12}}}1=x{\displaystyle 1=x} To make sure your answer is correct, substitute your solution back into the original equation. If the equation is true, your answer is correct. For example, if 1=x{\displaystyle 1=x}, substitute 1 for the variable in the equation and calculate:2(10−2x)=4(2x+2){\displaystyle 2(10-2x)=4(2x+2)}2(10−2(1))=4(2(1)+2){\displaystyle 2(10-2(1))=4(2(1)+2)}2(10−2)=4(2+2){\displaystyle 2(10-2)=4(2+2)}20−4=8+8{\displaystyle 20-4=8+8}16=16{\displaystyle 16=16}

summary: Apply the distributive property, if necessary. Cancel the variable on one side of the equation. Keep the equation balanced. Simplify the equation by combining like terms. Move the constants to one side of the equation, if necessary. Cancel the variable’s coefficient. Check your work.


Summarize the following:
Perfect with tea or coffee, simply add 1 teaspoon cinnamon and 1/2 teaspoon nutmeg to the flour for a tasty spiced pastry. You could also consider a 1/2 teaspoon of allspice, cloves, or orange zest to suit your preferences. Simply mix in the oats after cutting the butter and flour. You may need to add an extra 1/2 cup of milk in order to blend the oats in with the dough, as they will soak up the liquid quickly. This simple, scone-like treat is easy to make. Simply add the apples and cinnamon in place of the dried fruit. Tasting a bit like unsweetened coconut macaroons, adding coconut takes your rock cakes to the next level. Mix the coconut in with the dried fruit. Some people think that everything is better with chocolate, and they will find compelling evidence in chocolate rock cakes. Simply add an equal amount of semi-sweet chocolate chips when you would add dried fruit. Squeeze half a lemon or add a splash of orange juice in place of milk to add a little tang to your rock cake.  You can also add 1/2 cup lemon curd for sweet, moist cakes that are similar to scones. Grate 1 to 2 teaspoons of lemon or orange rind into the dough for a more pronounced citrus flavor.

summary: Add cinnamon and nutmeg for a spiced rock cake. Add 1 cup of oats for classic British rock cakes. Add chopped apples and cinnamon for apple cakes. Add shredded coconut for Jamaican rock cakes. Substitute chocolate for dried fruit for sweeter cakes. Add lemon juice or orange juice for a moist citrus rock cake.


Summarize the following:
Recording behaviors as they occur can help you see a pattern. You can see when a student is most likely to misbehave. You can identify any triggers that may be causing the difficult behavior.  Keep a notebook to record difficult behaviors. Note all the details of the behavior, when it occurred, and any circumstances surrounding the incident. Look for patterns. Does the student seem to act out at a particular time during the day? Maybe a student acts out just before recess. This could be because the student is anxious to get out of the classroom. This student may need help regulating his or her energy. Once you know when problem behaviors occur, increase supervision during this time. This can help you eliminate behavior issues.  You can monitor your class more closely during certain times of the day. Group work just before recess, for example, may require additional supervision. If you have any classroom assistants, ask for their help here. Have them monitor students closely when they're likely to act out. Students often respond better to positive reinforcement than negative reinforcement. Instead of always scolding students for poor behavior, work on praising students for positive behavior.  Always praise students for following rules. Do so immediately after the good behaviors occur. A lot of students crave praise and approval from their teacher. Students with behavior issues may be more likely to change if they see they gain favor by following rules. For example, you can say something like, "Harper, I really like how you waited for me to finish explaining before asking a question. It makes the classroom run smoother when everyone takes turns talking." More often than not, students are acting out for a reason. You want to make sure you identify underlying problems so they can be dealt with appropriately.  A student who is behaving poorly may have a health problem, an issue at home, a mental health issue, or may be acting out due to academic difficulties. If a student's behavior does not improve with regular intervention, there may be something else going on. You may have to have a sit down talk with a student whose behavior is not improving. Ask him or her open-ended questions, like, "Is there a reason you're having trouble concentrating." This gives the student the opportunity to open up on what is preventing him or her from achieving academic success.
summary: Record problem behaviors. Supervise students more closely when they're likely to lash out. Reinforce positive behaviors. Identify any underlying problems.