A scatter plot is shown on the coordinate plane. Which of these most closely approximates a line of best fit for the data in the scatter plot?

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GRADE 4 Module 6 Lesson 3. Interpret Remainders This PowerPoint file contains instructional aids for teachers who have purchased Into Math. It is intended to be projected to students and used in conjunction with the Student Edition and manipulatives as needed. These slides can be used to move the conversation forward in the classroom, but they should not serve as a replacement for student-centered, collaborative conversations in which students have the space they need to find an entry point, construct meaning, and build understanding. About the Slide Presentation Presenter View: Use the Presenter view to see notes while presenting. Customization: Add or delete content or notes to get the best learning experience for your classroom. 1 Problem of the Day. Which equations can be used to solve the following problem? Rita makes 40 bracelets and gives an equal number to 8 friends, including Veronica. Veronica gives 2 of the bracelets that she received to her sister. How many bracelets does Veronica have left? A. 40 – 8 = 32 32 ÷ 2 = 16 B. 40 ÷ 8 = 5 5 + 2 = 7 C. 8 + 2 = 10 40 ÷ 10 = 4 D. 40 ÷ 8 = 5 5 – 2 = 3 2 I Can. I Can solve a division problem and interpret the remainder in the context of the problem. 3 Spark Your Learning. Aiden is building solar toy cars in his science club. The cars collect and use energy from the sun for power. Aiden buys 18 wheels. Each car needs 4 wheels. How many cars can Aiden build? Show your thinking. 4 Turn and Talk. What is the remainder in this problem? What does the remainder mean? Professional Development note: Use the Professional Learning Cards to provide language routines that may help students access the meaning of the problem. 5 Build Understanding • Task 1 ACTIVITY. There are 57 students going to the science museum. Each van can take 5 students. How many vans are needed to take all the students? Use a visual model to show how the students are divided into groups of 5. 6 Turn and Talk. How can you use the whole-number quotient and remainder to answer these questions? How many vans will be full? How many students will ride in the van that is not full? Professional Development note: Use the Professional Learning Cards to provide language routines that may help students access the meaning of the problem. 7 Step It Out • Task 2 ACTIVITY.. Amanda has 73 inches of wire for a science experiment. She needs to cut all the wire into 8 identical pieces. How many inches long will each piece be? 8 Turn and Talk. Why is this problem a good situation to write the remainder as a fraction? Professional Development note: Use the Professional Learning Cards to provide language routines that may help students access the meaning of the problem. 9 Check Understanding. 1. Maya needs 44 batteries for smoke alarms. The batteries come in packs of 6. How many packs does Maya need to buy? For 44 ÷ 6, the whole-number quotient is ____ and the remainder is ____. Maya needs to buy ____ packs. Circle how you interpreted the remainder to solve the problem. 10 I Can Scale. 4 I can explain how to solve a division problem and interpret the remainder in the context of the problem. 3 I can solve a division problem and interpret the remainder in the context of the problem. 2 I can solve a division problem and identify the whole-number quotient and the remainder. 1 I can solve a division problem with a remainder. 11 Exit Ticket. Mr. Jenkins’ class is giving speeches during a 46-minute class. Each student will be able to talk for 4 minutes. How many students can give speeches? Justify your answer.

PHOTOSYNTHESIS LIGHT DEPENDENT REACTION 1. Photosystem II (PSII) – Light Absorption & Water Splitting • Light energy (photons) excites electrons in chlorophyll molecules. • These high-energy electrons leave PSII and are passed into the electron transport chain (ETC). • Meanwhile, water molecules are split (photolysis) into: o O₂ (released as a by-product into the atmosphere) o H⁺ ions (protons, which build up inside the thylakoid) o Electrons (e⁻), which replace the ones lost by PSII. 2. Electron Transport Chain (ETC) • Excited electrons move through protein carriers embedded in the thylakoid membrane. • As they move, their energy pumps H⁺ ions into the thylakoid space, creating a proton gradient (high H⁺ inside, low outside). 3. ATP Production (ATP Synthase) • The buildup of H⁺ ions acts like a “waterfall” of potential energy. • These protons flow back across the membrane through ATP synthase, a protein complex that acts like a turbine. • This flow drives the conversion of ADP + Pi → ATP, which provides energy for the Calvin cycle. 4. Photosystem I (PSI) • Electrons arriving from the ETC enter PSI. • Sunlight excites them again, boosting them to a higher energy level. 5. NADPH Production • The energized electrons are transferred to NADP⁺. • Along with a proton (H⁺), this forms NADPH, another energy carrier. • NADPH is then delivered to the Calvin cycle to help build glucose. End Products of Light-Dependent Reactions: • ATP (energy source for Calvin cycle) • NADPH (reducing power for glucose synthesis) • O₂ (released into the atmosphere as waste) Light-Independent Reactions (Calvin Cycle) • These reactions do not directly require sunlight. • They occur in the stroma of the chloroplast (the fluid-filled space surrounding the thylakoids). • The inputs are ATP and NADPH (from light-dependent reactions) and CO₂ (from the atmosphere). • The outputs are glucose (C₆H₁₂O₆) and other carbohydrates. Think of the Calvin cycle as a factory that uses the energy and “raw materials” made in Stage I (ATP & NADPH) to build sugars. The 3 Main Steps of the Calvin Cycle 1. Carbon Fixation • CO₂ from the atmosphere enters the chloroplast and diffuses into the stroma. • Each CO₂ molecule attaches to a 5-carbon sugar called RuBP (ribulose-1,5-bisphosphate). • This reaction is catalyzed by the enzyme RuBisCO (Ribulose-1,5-bisphosphate carboxylase/oxygenase — the most abundant enzyme on Earth!). • The result is a short-lived 6-carbon compound, which immediately splits into two 3-carbon molecules called 3-PGA (3-phosphoglycerate). Summary: CO₂ + RuBP → 2 × 3-PGA 2. Reduction Phase • The 3-PGA molecules are “energized” and converted into G3P (glyceraldehyde-3-phosphate), a more energy-rich 3-carbon sugar. • This transformation requires: o ATP (provides energy) o NADPH (provides high-energy electrons and hydrogen atoms). • Some of the G3P molecules will eventually be combined to form glucose and other sugars. Summary: 3-PGA + ATP + NADPH → G3P 3. Regeneration of RuBP • Not all G3P molecules leave the cycle. Most of them are used to regenerate RuBP so the cycle can continue. • This regeneration also requires ATP. • For every 3 turns of the cycle, 5 G3P molecules are recycled to regenerate 3 molecules of RuBP. Summary: G3P + ATP → RuBP The Full Cycle Balance • To make one G3P molecule that can exit the cycle (and later form glucose), the cycle must run 3 times, fixing 3 molecules of CO₂. • To make one glucose molecule (C₆H₁₂O₆), the cycle must run 6 times (since glucose needs 6 carbon atoms). Inputs (for 1 glucose): • 6 CO₂ • 18 ATP • 12 NADPH Outputs: • 1 glucose (C₆H₁₂O₆) • 18 ADP + 18 Pi • 12 NADP⁺ Day vs Night Clarification • The Calvin Cycle is called light-independent, but that doesn’t mean it only happens at night. • It usually happens during the day because it depends on ATP and NADPH, which are only produced in light-dependent reactions (when sunlight is available). Simplified Analogy • Carbon fixation = The factory brings in CO₂ as raw material. • Reduction = Workers use energy (ATP & NADPH) to shape the raw material into useful products (G3P). • Regeneration = Some products are recycled to keep the factory running (RuBP is re-formed). • Output = After enough cycles, the factory produces glucose, the “food” of the plant.

Cell Size Cells differ not only in their shape but also in their size. A few types of cells are large enough to be seen by the unaided human eye. For example, the nerve cells that extend from a giraffe’s spinal cord to its foot can be 2 m (about 6 1/2 ft) long. A human egg cell is about the size of the period at the end of this sentence. Most cells, how- ever, are only 10 to 50 μm in diameter, or about 1/500 the size of the period at the end of this sentence. The size of a cell is limited by the relationship of the cell’s outer surface area to its volume, or its surface area–to-volume ratio. As a cell grows, its volume increases much faster than its surface area does, as shown in Figure 4-5. This trend is important because the materials needed by a cell (such as nutrients and oxygen) and the wastes produced by a cell (such as carbon dioxide) must pass into and out of the cell through its surface. If a cell were to become very large, the volume would increase much more than the surface area. Therefore, the surface area would not allow materials to enter or leave the cell quickly enough to meet the cell’s needs. As a result, most cells are microscopic in size. Comparing Surface Cells Materials microscope, prepared slides of plant (dicot) stem and ani- mal (human) skin, pencil, paper Procedure Examine slides by using medium magnification (100). Observe and draw the sur- face cells of the plant stem and the animal skin. Analysis How do the surface cells of each organism differ from the cells beneath the surface cells? What is the function of the surface cells? Explain how surface cells are suited to their function based on their shape. Quick Lab Small cells can exchange substances more readily than large cells because small objects have a higher surface area–to-volume ratio. FIGURE 4-5 mb06se_csfs02.qxd 5/18/07 10:54 AM Page 73 74 CHAPTER 4 BASIC PARTS OF A CELL Despite the diversity among cells, three basic features are common to all cell types. All cells have an outer boundary, an interior sub- stance, and a control region. Plasma Membrane The cell’s outer boundary, called the plasma membrane (or the cell membrane), covers a cell’s surface and acts as a barrier between the inside and the outside of a cell. All materials enter or exit through the plasma membrane. The surface of a plasma mem- brane is shown in Figure 4-6a. Cytoplasm The region of the cell that is within the plasma membrane and that includes the fluid, the cytoskeleton, and all of the organelles except the nucleus is called the cytoplasm. The part of the cytoplasm that includes molecules and small particles, such as ribosomes, but not membrane-bound organelles is the cytosol. About 20 percent of the cytosol is made up of protein. Control Center Cells carry coded information in the form of DNA for regulating their functions and reproducing themselves. The DNA in some types of cells floats freely inside the cell. Other cells have a mem- brane-bound organelle that contains a cell’s DNA. This membrane- bound structure is called the nucleus. Most of the functions of a eukaryotic cell are controlled by the cell’s nucleus. The nucleus is often the most prominent structure within a eukaryotic cell. It maintains its shape with the help of a protein skeleton called the nuclear matrix. The nucleus of a typical animal cell is shown in Figure 4-6b. Most animal cells have a cell membrane, a nucleus, and a variety of other organelles embedded in a watery substance. The surface of the cell membrane can be seen in (a). The organelles inside the cell are labeled in the diagram (b). FIGURE 4-6 (a) (b) Mitochondrion Microfilaments Lysosome Golgi apparatus Smooth ER Ribosomes Cell membrane Microtubules Rough ER Nuclear pore Nuclear envelope Nucleolus Nucleus Copyright © by Holt, Rinehart and Winston. All rights reserved. Cell wall Ribosome Cell membrane Peptidoglycan Pili Flagellum DNA CELL STRUCTURE AND FUNCTION 75 A prokaryotic cell lacks a membrane- bound nucleus and membrane-bound organelles. Most prokaryotic cells are much smaller than eukaryotic cells are. FIGURE 4-7 A white blood cell (eukaryotic) changes shape as it attacks purple- stained bacterial cells that are much smaller (prokaryotic). FIGURE 4-8 TWO BASIC TYPES OF CELLS Fossil evidence suggests that the earliest cells on Earth were simple cells similar to some present-day bacteria. As cells evolved, they differentiated into two major types: prokaryotes and eukaryotes. Prokaryotes Prokaryotes (proh-KAR-ee-OHTS) are organisms that lack a membrane- bound nucleus and membrane-bound organelles. Although prokaryotic cells lack a nucleus, their genetic information—in the form of DNA—is often concentrated in a part of the cell called the nucleoid. Figure 4-7 shows a typical prokaryotic cell. Prokaryotes are divided into two domains: Bacteria and Archaea (ahr-KEE-uh). The domain Bacteria includes organisms that are similar to the first cellular life-forms. The domain Archaea includes organisms that are thought to be more closely related to eukaryotic cells found in all other kingdoms of life. Eukaryotes Organisms made up of one or more cells that have a nucleus and membrane-bound organelles are called eukaryotes (yoo-KAR-ee-OHTS). Eukaryotic cells also have a variety of subcellular structures called organelles, well-defined, intracellular bodies that perform specific functions for the cell. Many organelles are surrounded by a mem- brane. The organelles carry out cellular processes just as a person’s pancreas, heart, and other organs carry out a person’s life processes. Eukaryotic cells are generally much larger than prokary- otic cells, as seen in Figure 4-8, which shows a white blood cell (eukaryote) destroying tiny bacterial cells (prokaryotes).

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